Fq-Linear Cyclic Codes over Fqm: DFT Characterization
Codes over F[inqm that form vector spaces over F q are called Fq-linear codes over Fqm. Among these we consider only cyclic codes and call them F q -linear cyclic codes (F q LC codes) over [itFqm. 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 F q LC codes is obtained using Discrete Fourier Transform (DFT) over an extension field of F q m. We show how one 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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