Construction of codes by lattice valued fuzzy sets.
Construction of Optimal Linear Codes by Geometric Puncturing
Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4.∗This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 24540138.
Constructions of digital nets
Cycle indicators of linear groups and enumeration of linear codes. (Zyklenzeiger linearer Gruppen und Abzählung linearer Codes.)
Digital (t,m,s)-nets and the spectral test
Distances invariantes et L-cliques sur certains demi-groupes finis
Divisible Codes - A Survey
This paper surveys parts of the study of divisibility properties of codes. The survey begins with the motivating background involving polynomials over finite fields. Then it presents recent results on bounds and applications to optimal codes.
Dual codes of projective planes of order 25.
Duality for digital nets and its applications
Évariste Galois et la planète Mars : introduction à la théorie algébrique du codage
Exploring invariant linear codes through generators and centralizers
We investigate a -invariant linear code over the finite field where is a group of linear transformations. We show that if is a noncyclic abelian group and , then the code is the sum of the centralizer codes where is a nonidentity element of . Moreover if is subgroup of such that , , then dim is known when the dimension of is known for each subgroup of . In the last few sections we restrict our scope of investigation to a special class of invariant codes, namely affine...
Hierarchical models, marginal polytopes, and linear codes
In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.
Improvements on the Juxtaposing Theorem
A new class of binary constant weight codes is presented. We establish new lower bound and exact values on A(n1 +n2; 2(a1 +a2); n2) ≥ min {M1;M2}+1, if A(n1; 2a1; a1 +b1) = M1 and A(n2; 2b2; a2 +b2) = M2, in particular, A(30; 16; 15) = 16 and A(33; 18; 15) = 11.
Les codes géométriques de Goppa
Linear codes over finite chain rings.
Lower bounds for the football pool problem for 7 and 8 matches.
MacWilliams identities and matroid polynomials.
Minimal Codewords in Linear Codes
2000 Mathematics Subject Classification: 94B05, 94B15.Cyclic binary codes C of block length n = 2^m − 1 and generator polynomial g(x) = m1(x)m2^s+1(x), (s, m) = 1, are considered. The cardinalities of the sets of minimal codewords of weights 10 and 11 in codes C and of weight 12 in their extended codes ^C are determined. The weight distributions of minimal codewords in the binary Reed-Muller codes RM (3, 6) and RM (3, 7) are determined. The applied method enables codes with larger parameters to...
Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)
Modular invariance property of association schemes is recalled in connection with our joint work with François Jaeger. Then we survey codes over discussing how codes, through their (various kinds of) weight enumerators, are related to (various kinds of) modular forms through polynomial invariants of certain finite group actions and theta series. Recently, not only codes over an arbitrary finite field but also codes over finite rings and finite abelian groups are considered and have been studied...
Necessary and Sufficient Conditions for the Extendability of Ternary Linear Codes
We give the necessary and sufficient conditions for the extendability of ternary linear codes of dimension k ≥ 5 with minimum distance d ≡ 1 or 2 (mod 3) from a geometrical point of view.