Designs, Codes and Cryptography

, Volume 46, Issue 1, pp 45–56 | Cite as

On perfect p-ary codes of length p + 1

  • Olof Heden


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.


Perfect codes Redei Theorem 

AMS Classification



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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of MathematicsKTHStockholmSweden

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