A Z2Z4-linear Hadamard code of length α+2β = 2 is a binary Hadamard code which is the Gray map image of a Z2Z4-additive code with α binary coordinates and β quaternary coordinates. It is known that there are exactly b t−1 2 c and b t 2 c nonequivalent Z2Z4-linear Hadamard codes of length 2, with α = 0 and α 6= 0, respectively, for all t ≥ 3. In this paper, it is shown that each Z2Z4-linear Hada...

Let [n, k, d]q code be a linear code of length n, dimension k and Hamming minimum distance d over GF(q). In this paper record-breaking codes with parameters [30, 10, 15]5, [33, 11, 16]5, [41, 10, 22]5, [24, 14, 8]7, [40, 11, 22]7, [60, 10, 38]7, [60, 13, 34]7, [88, 8, 63]7, [96, 11, 64]7, [96, 13, 61]7 and [96, 15, 58]7 are constructed.

We study the combinatorial function L(k, q), the maximum number of nonzero weights a linear code of dimension k over Fq can have. We determine it completely for q = 2, and for k = 2, and provide upper and lower bounds in the general case when both k and q are ≥ 3. A refinement L(n, k, q), as well as nonlinear analogues N(M, q) and N(n,M, q), are also introduced and studied.

GivenS|R a finite Galois extension of finite chain rings andB anS-linear code we define twoGalois operators, the closure operator and the interior operator. We proof that a linear code is Galois invariant if and only if the row standard form of its generator matrix has all entries in the fixed ring by the Galois group and show a Galois correspondence in the class of S-linear codes. As applicati...

Let A(n, d, w) be the largest possible size of an (n, d, w) constant-weight binary code. By adding new constraints to Delsarte linear programming, we obtain twenty three new upper bounds on A(n, d, w) for n ≤ 28. The used techniques allow us to give a simple proof of an important theorem of Delsarte which makes linear programming possible for binary codes.

Completely regular codes with covering radius ρ = 1 must have minimum distance d ≤ 3. For d = 3, such codes are perfect and their parameters are well known. In this paper, the cases d = 1 and d = 2 are studied and completely characterized when the codes are linear. Moreover, it is proven that all these codes are completely transitive.

The present note establishes the equivalence of Mac Williams identities for an additive code C and its dual C to Polarized Riemann-Roch Conditions on their ζ-functions. In such a way, the duality of additive codes appears to be a polarized form of the Serre duality on a smooth irreducible projective curve.

A complete extension theorem for linear codes over a module alphabet and the symmetrized weight composition is proved. It is shown that an extension property with respect to arbitrary weight function does not hold for module alphabets with a noncyclic socle.

The codes obtained as the shortened binary image of linear codes over GF(2m) are studied in detail. Their dimension is computed and it is shown that they may be used as unequal error proteetion codes.