A class of constacyclic codes are generalized Reed-Solomon codes

10/21/2022

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by   Hongwei Liu, et al.

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Maximum distance separable (MDS) codes are optimal in the sense that the minimum distance cannot be improved for a given length and code size. The most prominent MDS codes are generalized Reed-Solomon (GRS) codes. The square 𝒞^2 of a linear code 𝒞 is the linear code spanned by the component-wise products of every pair of codewords in 𝒞. For an MDS code 𝒞, it is convenient to determine whether 𝒞 is a GRS code by determining the dimension of 𝒞^2. In this paper, we investigate under what conditions that MDS constacyclic codes are GRS. For this purpose, we first study the square of constacyclic codes. Then, we give a sufficient condition that a constacyclic code is GRS. In particular, We provide a necessary and sufficient condition that a constacyclic code of a prime length is GRS.