Ranks of q-Ary 1-Perfect Codes |
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| Authors: | Kevin T. Phelps Mercè Villanueva |
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| Affiliation: | (1) Discrete & Statistical Sciences, Auburn University, Auburn, Al, 36849-5307;(2) Dept. d'Informàtica, Universitat Autònoma de Barcelona, 08193- Bellaterra, Spain |
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| Abstract: | ![]()
The rank of a q-ary code C of length n, r(C), isthe dimension of the subspace spanned by C. We establish the existence of q-ary 1-perfectcodes of length  for m  4 and r(C)= n – m + s for each s  {1, ,m}. This is a generalization of the binary case proved by Etzion and Vardy in[4]. |
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| Keywords: | q-ary perfect code |
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