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Start Over Search Limiters Peer Reviewed Topic cyclic code Publication Year Range More than 50 years ago Language english

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1. On the nonexistence of perfect 2- and 3-Hamming-error-correcting codes over GF(q)

Author

J.H. van Lint and Mathematics and Computer Science

Subjects
Discrete mathematics, Code (set theory), Ternary Golay code, Perfect power, Binary Golay code, Cyclic code, Diophantine equation, General Engineering, ComputingMilieux_LEGALASPECTSOFCOMPUTING, Prime power, Hamming code, Engineering(all), Mathematics
Abstract

There are two well-known necessary conditions for the existence of a perfect error-correcting code. Combination of these leads to a Diophantine equation. It is proved that this equation has no solutions for n > 2, q > 3 (q a prime power) in the case of two errors. Furthermore we prove that the Golay (23, 12) code is the only nontrivial perfect 3-error-correcting code over any alphabet GF(q).

Published
1970