On the structure of optimal error-correcting codes. (English) Zbl 0935.94026
Summary: G. A. Kabatyanskij and V. I. Panchenko [Probl. Inf. Transm. 24, No. 4, 261-272 (1988); translation from Probl. Peredachi Inf. 24, 3-16 (1988; Zbl 0679.94015)] asked whether two sets of size 10 consisting of binary 7-tuples exist, such that all 100 sums with one element from each set are distinct. This question is here answered in the negative by showing that the existence of such sets would imply the existence of a binary single-error-correcting code of length 9 and size 40 (which is unique) with a certain property, which such a code does not have.
MSC:
| 94B05 | Linear codes (general theory) |
Keywords:
error-correcting codesCitations:
Zbl 0679.94015References:
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| [2] | Kabatyanskii, G. A.; Panchenko, V. I., Unit sphere packings and coverings of the Hamming space, Probl. Inform. Trans., 24, 261-272 (1988) · Zbl 0679.94015 |
| [3] | LeVan, M.; Phelps, K. T., Computing the kernel of a non-linear code, J. Comb. Math. Comb. Comput., 20, 237-241 (1996) · Zbl 0846.94021 |
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| [5] | Östergärd, P. R.J.; Kaikkonen, M. K., New single-error-correcting codes, IEEE Trans. Inform. Theory, 42, 1261-1262 (1996) · Zbl 0864.94029 |
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