Cocyclic Butson Hadamard matrices and Codes over Zn via the Trace Map
نویسندگان
چکیده
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 to construct cocyclic Butson Hadamard matrices of order nm for all n and m and linear and non-linear codes over Zn.
منابع مشابه
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.
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