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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.
Li et al. (Fri,) studied this question.