Abstract
Let p be a prime number and assume p ≥ 5. We will use a result of L. Redéi to prove, that every perfect 1-error correcting code C of length p + 1 over an alphabet of cardinality p, such that C has a rank equal to p and a kernel of dimension p − 2, will be equivalent to some Hamming code H. Further, C can be obtained from H, by the permutation of the symbols, in just one coordinate position.
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Communicated by V.A. Zinoviev.
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Heden, O. On perfect p-ary codes of length p + 1. Des. Codes Cryptogr. 46, 45–56 (2008). https://doi.org/10.1007/s10623-007-9133-y
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DOI: https://doi.org/10.1007/s10623-007-9133-y