Advances in Mathematics of Communications (AMC)

On the structure of non-full-rank perfect $q$-ary codes
Pages: 149 - 156, Volume 5, Issue 2, May 2011

doi:10.3934/amc.2011.5.149      Abstract        References        Full text (319.3K)           Related Articles

Olof Heden - Department of Mathematics, KTH, S-100 44 Stockholm, Sweden (email)
Denis S. Krotov - Sobolev Institute of Mathematics, Mechanics and Mathematics Department, Novosibirsk State University, Novosibirsk, Russian Federation (email)

1 S. W. Golomb and E. C. Posner, Rook domains, Latin squares, and error-distributing codes, IEEE Trans. Inf. Theory, 10 (1964), 196-208.       
2 O. Heden, On the classification of perfect binary $1$-error correcting codes, preprint, TRITA-MAT-2002-01, KTH, Stockholm, 2002.
3 D. S. Krotov, Combining construction of perfect binary codes, Probl. Inf. Transm., 36 (2000), 349-353; Translated from Probl. Peredachi Inf., 36 (2000), 74-79.       
4 D. S. Krotov, V. N. Potapov and P. V. Sokolova, On reconstructing reducible $n$-ary quasigroups and switching subquasigroups, Quasigroups Relat. Syst., 16 (2008), 55-67.       
5 C. F. Laywine and G. L. Mullen, "Discrete Mathematics Using Latin Squares,'' Wiley, New York, 1998.       
6 A. V. Los', Construction of perfect $q$-ary codes by switchings of simple components, Probl. Inf. Transm., 42 (2006), 30-37; Translated from Probl. Peredachi Inf., 42 (2006), 34-42.       
7 M. Mollard, A generalized parity function and its use in the construction of perfect codes, SIAM J. Algebraic Discrete Methods, 7 (1986), 113-115.       
8 K. T. Phelps, A general product construction for error correcting codes, SIAM J. Algebraic Discrete Methods, 5 (1984), 224-228.       
9 K. T. Phelps, A product construction for perfect codes over arbitrary alphabets, IEEE Trans. Inf. Theory, 30 (1984), 769-771.       
10 V. N. Potapov and D. S. Krotov, Asymptotics for the number of $n$-quasigroups of order $4$, Sib. Math. J., 47 (2006), 720-731; Translated from Sib. Mat. Zh., 47 (2006), 873-887.       
11 V. N. Potapov and D. S. Krotov, On the number of $n$-ary quasigroups of finite order (in Russian), Diskretnaya Matematika, 23 (2011), accepted; to be translated in Discrete Math. Appl., 21; arXiv:0912.5453

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