Abstract
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.
This work was partly supported by CSIR, India, through Research Grant (22(0298)/99/EMR-II) to B. S. Rajan
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Kumar Dey, B., Sundar Rajan, B. (2001). F q -Linear Cyclic Codes over F q m: DFT Characterization. In: Boztaş, S., Shparlinski, I.E. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2001. Lecture Notes in Computer Science, vol 2227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45624-4_7
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