| 1. |
- Avgustinovich, S. V., et al.
(författare)
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On intersection problem for perfect binary codes
- 2006
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Ingår i: Designs, Codes and Cryptography. - : Springer Science and Business Media LLC. - 0925-1022 .- 1573-7586. ; 39:3, s. 317-322
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Tidskriftsartikel (refereegranskat)abstract
- The main result is that to any even integer q in the interval 0 <= q <= 2(n+1-2) (log(n+1)), there are two perfect codes C-1 and C-2 of length n = 2(m) -1, m >= 4, such that vertical bar C-1 boolean AND C-2 vertical bar = q.
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| 2. |
- Avgustinovich, S. V., et al.
(författare)
-
On partitions of an n-cube into nonequivalent perfect codes
- 2007
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Ingår i: Problems of Information Transmission. - : Pleiades Publishing Ltd. - 0032-9460 .- 1608-3253. ; 43:4, s. 310-315
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Tidskriftsartikel (refereegranskat)abstract
- We prove that for all n = 2(k)-1, k >= 5. there exists a partition of the set of all binary vectors of length n into pairwise nonequivalent perfect binary codes of length n with distance 3.
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| 3. |
- Avgustinovich, S. V., et al.
(författare)
-
On the structure of symmetry groups of Vasil'ev codes
- 2005
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Ingår i: Problems of Information Transmission. - : Springer Science and Business Media LLC. - 0032-9460 .- 1608-3253. ; 41:2, s. 105-112
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Tidskriftsartikel (refereegranskat)abstract
- The structure of symmetry groups of Vasil'ev codes is studied. It is proved that the symmetry group of an arbitrary perfect binary non-full-rank Vasil'ev code of length n is always nontrivial; for codes of rank n - log(n + 1) + 1, an attainable upper bound on the order of the symmetry group is obtained.
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| 4. |
- Avgustinovich, S. V., et al.
(författare)
-
The classification of some perfect codes
- 2004
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Ingår i: Designs, Codes and Cryptography. - 0925-1022 .- 1573-7586. ; 31:3, s. 313-318
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Tidskriftsartikel (refereegranskat)abstract
- Perfect 1-error correcting codes C in Z(2)(n), where n = 2(m) - 1, are considered. Let [C] denote the linear span of the words of C and let the rank of C be the dimension of the vector space [C]. It is shown that if the rank of C is n - m + 2 then C is equivalent to a code given by a construction of Phelps. These codes are, in case of rank n - m + 2, described by a Hamming code H and a set of MDS-codes D-h; h is an element of H, over an alphabet with four symbols. The case of rank n - m + 1 is much simpler: Any such code is a Vasil'ev code.
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