On Linear Codes over Z2s

Construction and classification of Z2s-linear Hadamard codes

The Z2s-additive and Z2Z4-additive codes are subgroups of Z n 2 and Z α 2 × Z β 4 , respectively. Both families can be seen as generalizations of linear codes over Z2 and Z4. A Z2s-linear (resp. Z2Z4-linear) Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s-additive (resp. Z2Z4-additive) code. It is known that there are exactly ⌊ t−1 2 ⌋ and ⌊ t 2⌋ nonequivalent Z2Z4-...

On the Kernel of \mathbb Z_2^s -Linear Hadamard Codes

The Z2s -additive codes are subgroups of Z n 2s , and can be seen as a generalization of linear codes over Z2 and Z4. A Z2s -linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s additive code. It is known that the dimension of the kernel can be used to give a complete classification of the Z4-linear Hadamard codes. In this paper, the kernel of Z2s -linear Hadamard...

On Some Linear Codes over Z2s

New Linear Codes over Zps via the Trace Map

The trace map has been used very successfully to generate cocyclic complex and Butson Hadamard matrices and simplex codes over Z4 and Z2s . We extend this technique to obtain new linear codes over Zps . It is worth nothing here that these codes are cocyclic but not simplex codes. Further we find that the construction method also gives Butson Hadamard matrices of order p.

Cocyclic Butson Hadamard matrices and Codes over Zn via the Trace Map

Over the past couple of years trace maps over Galois fields and Galois rings have been used very successfully to construct cocyclic Hadamard, complex Hadamard and Butson Hadamard matrices and subsequently to generate simplex codes over Z4,Z2s and Zp and new linear codes over Zps . Here we define a new map, the trace-like map and more generally the weighted-trace map and extend these techniques ...