Support Weight Enumerators and Coset Weight Distributions of Isodual Codes

Support Weight Enumerators and Coset Weight Distributions of Isodual Codes

In this paper various methods for computing the support weight enumerators of binary, linear, even, isodual codes are described. It is shown that there exist relationships between support weight enumerators and coset weight distributions of a code that can be used to compute partial information about one set of these code invariants from the other. The support weight enumerators and complete co...

Weight enumerators of self-orthogonal codes

Complete Weight Enumerators of Some Linear Codes

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime p, we determine the explicit complete weight enumerators of two classes of linear codes over Fp and they may have applications in cryptography and secret sharing schemes. Moreover, some examples are included to illustrate our results. Index Terms Linear code, complete weight e...

A construction of linear codes and their complete weight enumerators

Recently, linear codes constructed from defining sets have been studied extensively. They may have nice parameters if the defining set is chosen properly. Let m > 2 be a positive integer. For an odd prime p, let r = p and Tr be the absolute trace function from Fr onto Fp. In this paper, we give a construction of linear codes by defining the code CD = {(Tr(ax))x∈D : a ∈ Fr}, where D = { x ∈ Fr :...

Symmetries of weight enumerators and applications to Reed-Muller codes

Gleason's 1970 theorem on weight enumerators of self-dual codes has played a crucial role for research in coding theory during the last four decades. Plenty of generalizations have been proved but, to our knowledge, they are all based on the symmetries given by MacWilliams' identities. This paper is intended to be a first step towards a more general investigation of symmetries of weight enumera...