Families of Hadamard Z2Z4Q8-codes

الأصل · EN

A Z2Z4Q8-code is a non-empty subgroup of a direct product of copies of Z₂, Z₄ and Q₈ (the binary field, the ring of integers modulo 4 and the quaternion group on eight elements, respectively). Such Z2Z4Q8-codes are translation invariant propelinear codes as the well known Z₄-linear or Z₂Z₄-linear codes. In the current paper, we show that there exist "pure" Z2Z4Q8-codes, that is, codes that do not admit any abelian translation invariant propelinear structure. We study the dimension of the kernel and rank of the Z2Z4Q8-codes, and we give upper and lower bounds for these parameters. We give tools to construct a new class of Hadamard codes formed by several families of Z2Z4Q8-codes; we study and show the different shapes of such a codes and we improve the upper and lower bounds for the rank and the dimension of the kernel when the codes are Hadamard.