Fq-Linear Cyclic Codes over Fq: DFT Characterization

Codes over Fqm that form vector spaces over Fq are called Fq-linear codes over Fqm. Among these we consider only cyclic codes and call them Fq-linear cyclic codes (FqLC codes) over Fqm. This class of codes includes as special cases (i) group cyclic codes over elementary abelian groups (q = p, a prime), (ii) subspace subcodes of Reed-Solomon codes and (iii) linear cyclic codes over Fq (m=1). Transform domain characterization of FqLC codes is obtained using Discrete Fourier Transform (DFT) over an extension field of Fqm. We showho wone can use this transform domain structures to estimate a minimum distance bound for the corresponding quasicyclic code by BCH-like argument.

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