On nonsystematic perfect codes over finite fields

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Abstract

The nonsystematic perfect q-ary codes over finite field F q of length n = (q m − 1)/(q − 1) are constructed in the case when m ≥ 4 and q ≥ 2 and also when m = 3 and q is not prime. For q ≠ 3, 5, these codes can be constructed by switching seven disjoint components of the Hamming code H q n ; and, for q = 3, 5, eight disjoint components.

Key words

perfect code Hamming code Galois field nonsystematic code projective geometry component 

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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