A remark on full rank perfect codes |
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Authors: | Olof Heden |
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Institution: | Department of Mathematics, KTH, S-100 44 Stockholm, Sweden |
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Abstract: | Any full rank perfect 1-error correcting binary code of length n=2k-1 and with a kernel of dimension n-log(n+1)-m, where m is sufficiently large, may be used to construct a full rank perfect 1-error correcting binary code of length 2m-1 and with a kernel of dimension n-log(n+1)-k. Especially we may construct full rank perfect 1-error correcting binary codes of length n=2m-1 and with a kernel of dimension n-log(n+1)-4 for m=6,7,…,10.This result extends known results on the possibilities for the size of a kernel of a full rank perfect code. |
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Keywords: | Perfect codes Super dual Tiling |
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