Some optimal 픽q-linear codes over 픽ql.

Let 픽ql be a finite field of cardinality ql, where q is a power of a prime and l is a prime integer. An 픽q-linear code over 픽ql of length n is an 픽q-subspace of 픽qln. If an 픽q-linear code over 픽ql with parameters (n,qk,d H) meets the Singleton bound, i.e., dH = n −⌈k l ⌉ + 1, then it is called an MDS code. In this paper, by use of a Fourier matrix and a canonical form decomposition of constacyclic 픽q-linear codes over 픽ql, we construct some optimal 픽q-linear codes over 픽ql which have the same parameters as the MDS codes over 픽ql. [ABSTRACT FROM AUTHOR]