Mullin, Ronald C. (Ronald Cleveland) 1936
Overview
Works:  96 works in 183 publications in 3 languages and 1,600 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Author, Other 
Classifications:  QA268, 519.4 
Publication Timeline
.
Most widely held works by
Ronald C Mullin
The mathematical theory of coding by
Ian F Blake(
Book
)
16 editions published between 1974 and 2015 in English and held by 552 WorldCat member libraries worldwide
The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on selfdual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes
16 editions published between 1974 and 2015 in English and held by 552 WorldCat member libraries worldwide
The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on selfdual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes
An introduction to algebraic and combinatorial coding theory by
Ian F Blake(
Book
)
12 editions published between 1976 and 2015 in English and held by 427 WorldCat member libraries worldwide
An Introduction to Algebraic and Combinatorial Coding Theory
12 editions published between 1976 and 2015 in English and held by 427 WorldCat member libraries worldwide
An Introduction to Algebraic and Combinatorial Coding Theory
Finite fields : theory, applications, and algorithms : Fourth International Conference on Finite Fields Theory, Applications,
and Algorithms, August 1215, 1997, University of Waterloo, Ontario, Canada by International Conference on Finite Fields(
Book
)
19 editions published between 1998 and 2012 in English and held by 282 WorldCat member libraries worldwide
19 editions published between 1998 and 2012 in English and held by 282 WorldCat member libraries worldwide
Proceedings by Graph Theory, and Computing Louisiana Conference on Combinatorics(
Book
)
7 editions published between 1970 and 1971 in English and held by 83 WorldCat member libraries worldwide
7 editions published between 1970 and 1971 in English and held by 83 WorldCat member libraries worldwide
Applications of finite fields by
Ian F Blake(
)
4 editions published in 1993 in English and held by 61 WorldCat member libraries worldwide
The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. We shall focus our attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, we have not attempted to be encyclopedic. Among the topics studied are different methods of representing the elements of a finite field (including normal bases and optimal normal bases), algorithms for factoring polynomials over finite fields, methods for constructing irreducible polynomials, the discrete logarithm problem and its implications to cryptography, the use of elliptic curves in constructing public key cryptosystems, and the uses of algebraic geometry in constructing good errorcorrecting codes. To limit the size of the volume we have been forced to omit some important applications of finite fields. Some of these missing applications are briefly mentioned in the Appendix along with some key references
4 editions published in 1993 in English and held by 61 WorldCat member libraries worldwide
The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. We shall focus our attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, we have not attempted to be encyclopedic. Among the topics studied are different methods of representing the elements of a finite field (including normal bases and optimal normal bases), algorithms for factoring polynomials over finite fields, methods for constructing irreducible polynomials, the discrete logarithm problem and its implications to cryptography, the use of elliptic curves in constructing public key cryptosystems, and the uses of algebraic geometry in constructing good errorcorrecting codes. To limit the size of the volume we have been forced to omit some important applications of finite fields. Some of these missing applications are briefly mentioned in the Appendix along with some key references
Proceedings of the Louisiana conference on combinatorics graph theory and computing by
Graph Theory, and Computing Louisiana Conference on Combinatorics(
Book
)
11 editions published between 1970 and 1971 in English and held by 35 WorldCat member libraries worldwide
11 editions published between 1970 and 1971 in English and held by 35 WorldCat member libraries worldwide
The distribution of the frequency of occurrence of nucleotide subsequences based on their overlap capability by
Jane F Gentleman(
Book
)
4 editions published in 1988 in English and held by 29 WorldCat member libraries worldwide
DNA's genetic code can be represented as an alphabetic sequence composed of the four letters A, C, G, and T, which represent the four types of nucleotides  adnylic, cytidylic, guanylic, and thymidylic acid  of which DNA is composed. Now that these sequences have been identified for many genes and are available in computerreadable form, scientists can analyze these data and search for patterns in an attempt to learn more about the regulatory functions of the gene. One area of study is that of the frequency of occurrence of specific nucleotide subsequences (e.g., ACAC) within part or all of a nucleotide sequence. This paper derives the probability distribution of the frequency of occurrence of a subsequence within a nucleotide sequence, under the hypothesis that the four nucleotides occur at random and with equal probability. This distribution is nontrivial because different subsequences have different "overlap capability". For example, the subsequence AAAA can occur up to 17 times in a sequence of length 20 (which would happen if the sequence were composed solely of A's), but the subsequence ACGT cannot occur more than 5 times in a sequence of length 20. Thus, the frequency distributions are different for each type of overlap capability. It is of interest to assess and compare the degree of nonrandomness for different subsequences or among different portions of a sequence; the existence and degree of nonrandomness may be related to the type and degree of functionality of a nucleotide (sub)sequence. Using the frequency distributions provided here, exact significance tests of the hypothesis of randomness can be performed. An approximate test is also described for use with long sequences; this can be used to test a more general null hypothesis of nucleotides occurring with unequal probabilities
4 editions published in 1988 in English and held by 29 WorldCat member libraries worldwide
DNA's genetic code can be represented as an alphabetic sequence composed of the four letters A, C, G, and T, which represent the four types of nucleotides  adnylic, cytidylic, guanylic, and thymidylic acid  of which DNA is composed. Now that these sequences have been identified for many genes and are available in computerreadable form, scientists can analyze these data and search for patterns in an attempt to learn more about the regulatory functions of the gene. One area of study is that of the frequency of occurrence of specific nucleotide subsequences (e.g., ACAC) within part or all of a nucleotide sequence. This paper derives the probability distribution of the frequency of occurrence of a subsequence within a nucleotide sequence, under the hypothesis that the four nucleotides occur at random and with equal probability. This distribution is nontrivial because different subsequences have different "overlap capability". For example, the subsequence AAAA can occur up to 17 times in a sequence of length 20 (which would happen if the sequence were composed solely of A's), but the subsequence ACGT cannot occur more than 5 times in a sequence of length 20. Thus, the frequency distributions are different for each type of overlap capability. It is of interest to assess and compare the degree of nonrandomness for different subsequences or among different portions of a sequence; the existence and degree of nonrandomness may be related to the type and degree of functionality of a nucleotide (sub)sequence. Using the frequency distributions provided here, exact significance tests of the hypothesis of randomness can be performed. An approximate test is also described for use with long sequences; this can be used to test a more general null hypothesis of nucleotides occurring with unequal probabilities
Distribution de la fréquence d'occurence des sousséquences de nucléotides, d'après leur capacité de chevauchement by
Jane F Gentleman(
Book
)
5 editions published in 1988 in French and held by 10 WorldCat member libraries worldwide
Le code générique de l'ADN peut être représenté sous forme d'une séquence alphabétique formée des lettres A, C, G, et T, qui représentent les quatre types de nuclétides qui composent l'ADN: acides adénylique, cytidilique, guanylique et thymidylique. Maintenant que ces séquences ont été identifiées pour de nombreux gènes et qu'on les possède sous une forme qui se prête au traitement par ordinateur, les scientifiques peuvent les analyser et y rechercher des structures, afin de tenter de mieux connaître les fonctions régulatrices du gène. L'un des sujets étudiés est la fréquence d'occurrence de sousséquences particulières de nucléotides (par ex. ACAC) dans l'ensemble, ou une partie, d'une séquence de nucléotides. Dans le présent document, on établit la distribution de probabilité de la fréquence d'occurrence d'une sousséquence dans une séquence de nucléotides, dans l'hypothèse où les quatre nucléotides apparaissent au hasard et avec une probabilité égale. La distribution n'est pas triviale puisque des sousséquences différentes présentent des "capacités de chevauchement" différentes. Par exemple, la sousséquence AAAA peut exister jusqu'à 17 fois dans une séquence de longueur 20 (ce qui se produira si la séquence est composée seulement de A), mais la sousséquence ACGT ne peut survenir plus de 5 fois dans une séquence de longueur 20. Ainsi, les distributions de fréquences sont différentes pour chaque type de capacité de chevauchement. Il est intéressant d'évaluer et de comparer le degré d'occurrence aléatoire pour différentes sousséquences, ou différentes parties d'une sousséquence; l'existence et le degré d'une occurrence nonaléatoire peuvent être reliés au type et au degré de fonctionnalité d'une (sous)séquence de nucléotides. Au moyen des distributions de fréquences présentées ici, on peut effectuer des tests de signification exacts de l'hypothèse d'une occurrence aléatoire. On décrit aussi un test approximatif qui convient aux longues séquences; ce test peut servir à vérifier l'hypothèse nulle plus générale selon laquelle les nucléotides se présentent avec des probabilités inégales
5 editions published in 1988 in French and held by 10 WorldCat member libraries worldwide
Le code générique de l'ADN peut être représenté sous forme d'une séquence alphabétique formée des lettres A, C, G, et T, qui représentent les quatre types de nuclétides qui composent l'ADN: acides adénylique, cytidilique, guanylique et thymidylique. Maintenant que ces séquences ont été identifiées pour de nombreux gènes et qu'on les possède sous une forme qui se prête au traitement par ordinateur, les scientifiques peuvent les analyser et y rechercher des structures, afin de tenter de mieux connaître les fonctions régulatrices du gène. L'un des sujets étudiés est la fréquence d'occurrence de sousséquences particulières de nucléotides (par ex. ACAC) dans l'ensemble, ou une partie, d'une séquence de nucléotides. Dans le présent document, on établit la distribution de probabilité de la fréquence d'occurrence d'une sousséquence dans une séquence de nucléotides, dans l'hypothèse où les quatre nucléotides apparaissent au hasard et avec une probabilité égale. La distribution n'est pas triviale puisque des sousséquences différentes présentent des "capacités de chevauchement" différentes. Par exemple, la sousséquence AAAA peut exister jusqu'à 17 fois dans une séquence de longueur 20 (ce qui se produira si la séquence est composée seulement de A), mais la sousséquence ACGT ne peut survenir plus de 5 fois dans une séquence de longueur 20. Ainsi, les distributions de fréquences sont différentes pour chaque type de capacité de chevauchement. Il est intéressant d'évaluer et de comparer le degré d'occurrence aléatoire pour différentes sousséquences, ou différentes parties d'une sousséquence; l'existence et le degré d'une occurrence nonaléatoire peuvent être reliés au type et au degré de fonctionnalité d'une (sous)séquence de nucléotides. Au moyen des distributions de fréquences présentées ici, on peut effectuer des tests de signification exacts de l'hypothèse d'une occurrence aléatoire. On décrit aussi un test approximatif qui convient aux longues séquences; ce test peut servir à vérifier l'hypothèse nulle plus générale selon laquelle les nucléotides se présentent avec des probabilités inégales
Proceedings of the second Louisiana Conference on Combinatorics, Graph Theory and Computing, Louisiana State University, Baton
Rouge, March 811, 1971 by
Graph Theory, and Computing (2, 1971, Baton Rouge, La.) Louisiana Conference on Combinatorics(
Book
)
5 editions published between 1971 and 1972 in English and held by 8 WorldCat member libraries worldwide
5 editions published between 1971 and 1972 in English and held by 8 WorldCat member libraries worldwide
On a problem of Hering concerning orthogonal covers of Kn by
Andrew Granville(
Book
)
1 edition published in 1995 in German and held by 4 WorldCat member libraries worldwide
1 edition published in 1995 in German and held by 4 WorldCat member libraries worldwide
Distribution of the frequency of occurrence of nucleotide subsequences based on their overlap capability by
Statistics Canada(
Book
)
2 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
Proceedings by Graph Theory, and Computing Louisiana Conference on Combinatorics(
Book
)
2 editions published between 1971 and 1972 in English and held by 4 WorldCat member libraries worldwide
2 editions published between 1971 and 1972 in English and held by 4 WorldCat member libraries worldwide
On orthogonal double covers of Kn and a conjecture of Chung and West by
HansDietrich O. F Gronau(
Book
)
1 edition published in 1995 in German and held by 3 WorldCat member libraries worldwide
1 edition published in 1995 in German and held by 3 WorldCat member libraries worldwide
Congressus numerantium(
Book
)
1 edition published in 1988 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 3 WorldCat member libraries worldwide
A characterization of the extremal distributions of optimal normal bases by
Ronald C Mullin(
Book
)
1 edition published in 1992 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1992 in English and held by 2 WorldCat member libraries worldwide
On packings of pairs by quintuples : v [identical with] 3,9 or 17(mod 20) by
Ronald C Mullin(
Book
)
2 editions published in 1992 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 2 WorldCat member libraries worldwide
Proceedings of the tenth Southeastern Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic University,
Boca Raton, April 26, 1979 by
Graph Theory, and Computing Southeastern Conference on Combinatorics(
Book
)
2 editions published in 1979 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1979 in English and held by 2 WorldCat member libraries worldwide
Near subgroups of groups by
D. G Hoffman(
Book
)
1 edition published in 1992 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1992 in English and held by 2 WorldCat member libraries worldwide
Distribution of the Frequency of Occurrence of Nucleotide Subsequences Based on Their Overlap Capability by
Statistics Canada(
Book
)
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
On [lambda]covers of pairs by quintuples : v odd by
W. H Mills(
Book
)
2 editions published between 1991 and 1992 in English and held by 2 WorldCat member libraries worldwide
2 editions published between 1991 and 1992 in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 Blake, Ian F. Author
 Mullen, Gary L. Other Editor
 Roselle, D. P. Editor
 Reid, Kenneth B. Editor
 Vanstone, Scott A.
 Gao, XuHong
 Menezes, Alfred J. Editor
 Yaghoobian, Tomik
 Gentleman, Jane F. Author
 Statistics Canada Analytical Studies Branch
Associated Subjects
Algebraic number theory Coding theory Combinatorial analysis Combinatorial analysisData processing Combinatorial packing and covering Computable functions Computational complexity Computer engineering Computer scienceMathematics DNA Electrical engineering Electronic data processing Electronic digital computers Engineering Engineering mathematics Finite fields (Algebra) Graphic methods Graph theory Graph theoryData processing Group theory Incomplete block designs Mathematical optimization NucleotidesAnalysis Numerical calculations