About some Hadamard full propelinear (2t,2,2)-codes : Rank and Kernel

A new subclass of Hadamard full propelinear codes is introduced in this article. We define the HFP(2t,2,2)-codes as codes with a group structure isomorphic to C₂t × C₂^2. Concepts such as rank and dimension of the kernel are studied, and bounds for them are established. For t odd, r=4t−1 and k=1. For t even, r≤2t and k≠2, and r=2t if and only if t≢0 (mod 4)

About a class of Hadamard propelinear codes

This article aims to explore the algebraic structure of Hadamard propelinear codes, which are not abelian in general but they have good algebraic and combinatorial properties. We construct a subclass of Hadamard propelinear codes which enlarges the family of the Hadamard translation invariant propelinear codes. Several papers have been devoted to the relations between difference sets, t-designs, cocyclic-matrices and Hadamard groups, and we present a link between them and a class of Hadamard propelinear codes, which we call full propelinear. Finally, as an exemplification, we provide a full propelinear structure for all Hadamard codes of length sixteen

Switching codes and designs

AbstractVarious local transformations of combinatorial structures (codes, designs, and related structures) that leave the basic parameters unaltered are here unified under the principle of switching. The purpose of the study is threefold: presentation of the switching principle, unification of earlier results (including a new result for covering codes), and applying switching exhaustively to some common structures with small parameters

Ranks and kernels of codes from generalized Hadamard matrices

The ranks and kernels of generalized Hadamard matrices are studied. It is proved that any generalized Hadamard matrix H(q, λ) over Fq , q > 3, or q = 3 and gcd(3, λ) ≠ 1, generates a self-orthogonal code. This result puts a natural upper bound on the rank of the generalized Hadamard matrices. Lower and upper bounds are given for the dimension of the kernel of the corresponding generalized Hadamard codes. For specific ranks and dimensions of the kernel within these bounds, generalized Hadamard codes are constructed