The non-existence of some perfect codes over non-prime power alphabets |
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Authors: | Olof Heden Cornelis Roos |
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Affiliation: | aDepartment of Mathematics, KTH, S-100 44 Stockholm, Sweden;bDepartment of Information Systems and Algorithms, Delft University of Technology, 2628 CD Delft, The Netherlands |
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Abstract: | Let denote the number of times the prime number p appears in the prime factorization of the integer q. The following result is proved: If there is a perfect 1-error correcting code of length n over an alphabet with q symbols then, for every prime number .This condition is stronger than both the packing condition and the necessary condition given by the Lloyd theorem, as it for example excludes the existence of a perfect code with the parameters (n,q,e)=(19,6,1). |
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Keywords: | Perfect codes |
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