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Nonexistence of some linear codes over the field of order four
Authors:Hitoshi Kanda  Tatsuya Maruta
Institution:Department of Mathematical Sciences, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan
Abstract:We consider the problem of determining n4(5,d), the smallest possible length n for which an n,5,d]4 code of minimum distance d over the field of order 4 exists. We prove the nonexistence of g4(5,d)+1,5,d]4 codes for d=31,47,48,59,60,61,62 and the nonexistence of a g4(5,d),5,d]4 code for d=138 using the geometric method through projective geometries, where gq(k,d)=i=0k?1dqi. This yields to determine the exact values of n4(5,d) for these values of d. We also give the updated table for n4(5,d) for all d except some known cases.
Keywords:Optimal linear code  Griesmer bound  Geometric method
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