A construction based on Legendre sequences is presented for a doubly-extended binary linear code of length 2p + 2 and dimension p+1. This code has a double circulant structure. For p = 4k +3, we obtain a doubly-even self-dual code. Another construction is given for a class of triply extended rate 1/3 codes of length 3p + 3 and dimension p + 1. For p = 4k + 1, these codes are doubly-even selfort...

We investigate the geometry of the support of small weight codewords of dual algebraic geometric codes on smooth complete intersections by applying the powerful tools recently developed by Alain Couvreur. In particular, by restricting ourselves to the case of Hermitian codes, we recover and extend previous results obtained by the second named author joint with Marco Pellegrini and Massimiliano ...

The main aim of this paper is to study LCD codes. Linear code with complementary dual(LCD) are those codes which have their intersection with their dual code as t0u. In this paper we will give rather alternative proof of Massey’s theorem[8], which is one of the most important characterization of LCD codes. Let LCDrn, ks3 denote the maximum of possible values of d among rn, k, ds ternary LCD cod...

Our purpose is to find an upper bound for the length of s-extremal codes over F2 (resp. F4) when d ≡ 2 (mod 4) (resp. d odd). This question is left open in [6], [2]. More precisely, we show that there is no s-extremal binary code of length n ≥ 21d− 82 if d > 6 and d ≡ 2 (mod 4). Similarly we show that there is no s-extremal additive F4 code of length n ≥ 13d− 26 if d > 1 and d is odd. We also d...

Klove, T., Support weight distribution of linear codes, Discrete Mathematics 106/107 (1992) 311-316. The main result of the paper is expressions for the support weight distributions of a linear code in terms of the support weight distributions of the dual code.

An (n, k) group code over a group G is a subset of G which forms a group under componentwise group operation and can be defined in terms of n — k homomorphisms from G to G. In this correspondence, the set of homomorphisms which define Maximum Distance Separable (MDS) group codes defined over cyclic groups are characterized. Each defining homomorphism can be specified by a set of k endomorpbisms...

A Z2Z4-additive code C ⊆ Z2 ×Zβ4 is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z2 and the set of Z4 coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. These codes can be identified as submodules of the Z4[x]-module Z2[x]/(x− 1)×Z4[x]/(x − 1). The parameters of a Z2Z4-additive cyclic code are stated i...

The Fq code of a symmetric (v,k,λ )design is a subspace generated by the incidence matrix of the symmetric design. In this paper, we examine the minimality of the codewords in the dual codeC⊥ of the binary codeC of a symmetric (v,k,λ )− design. So, we use the relationship between the minimum and maximum nonzero weights in the dual code C⊥ with the number of Fq.

The automorphism group of a binary doubly-even self-dual code is always contained in the alternating group. On the other hand, given a permutation group G of degree n there exists a doubly-even self-dual G-invariant code if and only if n is a multiple of 8, every simple self-dual F2G-module occurs with even multiplicity in F n 2 , and G is contained in the alternating group.

In analogy to cyclic codes, we study linear codes over finite fields obtained from left ideals in a quotient ring of a (non commutative) skew polynomial ring. The paper shows how existence and properties of such codes are linked to arithmetic properties of skew polynomials. This class of codes is a generalization of the θ-cyclic codes discussed in [1]. However θ-cyclic codes are performant repr...