On the Minimum Distances of Non-Binary Cyclic Codes

Authors:
Pascale Charpin;Aimo Tietäväinen;Victor Zinoviev
Affiliations:
INRIA, Codes Domaine de Voluceau-Rocquencourt BP 105 - 78153, Le Chesnay, France;Department of Mathematics and TUCS University of Turku FIN-20014 Turku, Finland;Institute for Problems of Information Transmission of the Russian Academy of Sciences Bol‘shoi Karetnyi 19 GSP-4, Moscow 101447, Russia
Venue:
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Year:
1999

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Abstract

We deal with the minimum distancesof q-ary cyclic codes of length q^m-1generated by products of two distinct minimal polynomials, givea necessary and sufficient condition for the case that the minimumdistance is two, show that the minimum distance is at most threeif q3, and consider also the case q=3.