|| On the Linearity and Structure of Z/2^s-Linear Simplex and MacDonald Codes
||Cristina Fernández-Córdoba, Carlos Vela, Mercè Villanueva, Universitat Autònoma de Barcelona, Spain|
||D2-S5-T2: Combinatorial & Algebraic Codes
||Tuesday, 13 July, 23:20 - 23:40
||Tuesday, 13 July, 23:40 - 00:00
Z/2^s-additive codes are subgroups of (Z/2^s)^n, and can be seen as a generalization of linear codes over Z2 and Z4. A Z/2^s-linear code is a binary code (not necessarily linear) which is the Gray map image of a Z/2^s-additive code. We considerZ/2^s-additive simplex codes of type α and β, which are a generalization over Z/2^s of the binary simplex codes. These codes are related to the Z/2^s-additive Hadamard codes. In this paper, we use this relationship to find a linear subcode of the corresponding Z/2^s-linear codes, called kernel, and a representation of these codes as cosets of this kernel. In particular, this also gives the linearity of these codes. Similarly, Z/2^s-additive MacDonald codes are defined for s >2, and equivalent results are obtained.