MacWilliams identities and matroid polynomials.
Maximal circular codes versus maximal codes
We answer to a question of De Luca and Restivo whether there exists a circular code which is maximal as circular code and not as code.
Maximal circular codes versus maximal codes
We answer to a question of De Luca and Restivo whether there exists a circular code which is maximal as circular code and not as code.
Messages parasites et codes synchronisants
Metric coset schemes revisited
An Abelian scheme corresponds to a special instance of what is usually named a Schur-ring. After the needed results have been quoted on additive codes in Abelian schemes and their duals, coset configurations, coset schemes, metric schemes and distance regular graphs, partition designs and completely regular codes, we give alternative proofs of some of those results. In this way we obtain a construction of metric Abelian schemes and an algorithm to compute their intersection matrices.
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...
Minimum distances of error-correcting codes in incidence rings.
Moderate-density CT burst error-locating linear codes
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...
Multi-covering radius for rank metric codes.