Some optimal 𝔽q-linear codes over 𝔽ql

Abstract

Let [Formula: see text] be a finite field of cardinality [Formula: see text], where [Formula: see text] is a power of a prime and [Formula: see text] is a prime integer. An [Formula: see text]-linear code over [Formula: see text] of length [Formula: see text] is an [Formula: see text]-subspace of [Formula: see text]. If an [Formula: see text]-linear code over [Formula: see text] with parameters [Formula: see text] meets the Singleton bound, i.e., [Formula: see text], then it is called an MDS code. In this paper, by use of a Fourier matrix and a canonical form decomposition of constacyclic [Formula: see text]-linear codes over [Formula: see text], we construct some optimal [Formula: see text]-linear codes over [Formula: see text] which have the same parameters as the MDS codes over [Formula: see text].