Bouyukliev, Iliya (2007)
Serdica Journal of Computing
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In this paper we present a developed software in the area of Coding Theory. Using it, codes with given properties can be classified. A part of this software can be used also for investigations (isomorphisms, automorphism groups) of other discrete structures-combinatorial designs, Hadamard matrices, bipartite graphs etc.
Alderson, T.L., Bruen, A.A. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Shaska, Tanush, Wang, Quanlong (2007)
Serdica Journal of Computing
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*Partially supported by NATO. We study Ca,b curves and their applications to coding theory. Recently, Joyner and Ksir have suggested a decoding algorithm based on the automorphisms of the code. We show how Ca;b curves can be used to construct MDS codes and focus on some Ca;b curves with extra automorphisms, namely y^3 = x^4 + 1, y^3 = x^4 - x, y^3 - y = x^4. The automorphism groups of such codes are determined in most characteristics.
Buyuklieva, Stefka (1999)
Serdica Mathematical Journal
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* This work was partially supported by the Bulgarian National Science Fund under Contract No. MM – 503/1995. New extremal binary self-dual codes of lengths 50 and 52 are constructed. Some of them are the first known codes with such weight enumerators. The structure of their automorphisms groups are shown.
Ward, Harold (2001)
Serdica Mathematical Journal
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This paper surveys parts of the study of divisibility properties of codes. The survey begins with the motivating background involving polynomials over finite fields. Then it presents recent results on bounds and applications to optimal codes.
Landjev, Ivan, Haralambiev, Kristiyan (2007)
Serdica Journal of Computing
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In 1965 Levenshtein introduced the deletion correcting codes and found an asymptotically optimal family of 1-deletion correcting codes. During the years there has been a little or no research on t-deletion correcting codes for larger values of t. In this paper, we consider the problem of finding the maximal cardinality L2(n;t) of a binary t-deletion correcting code of length n. We construct an infinite family of binary t-deletion correcting codes. By computer search, we construct t-deletion...
Yankov, Nikolay (2011)
Union of Bulgarian Mathematicians
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Николай Янков - Класифицирани са с точност до еквивалетност всички оптимални двоични самодуални [62, 31, 12] кодове, които притежават автоморфизъм от ред 7 с 8 независими цикъла при разлагане на независими цикли. Използвайки метода за конструиране на самодуални кодове, притежаващи автоморфизъм от нечетен прост ред е доказано, че съществуват точно 8 нееквивалентни такива кода. Три от получените кодове имат тегловна функция, каквато досега не бе известно да съществува. We...
Maruta, Tatsuya (2013)
Serdica Journal of Computing
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Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4. ∗This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 24540138.
Oya, Yusuke (2011)
Serdica Journal of Computing
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We prove the nonexistence of [g3(6, d), 6, d]3 codes for d = 86, 87, 88, where g3(k, d) = ∑⌈d/3i⌉ and i=0 ... k−1. This determines n3(6, d) for d = 86, 87, 88, where nq(k, d) is the minimum length n for which an [n, k, d]q code exists.
Eugeniusz Kuriata (2008)
International Journal of Applied Mathematics and Computer Science
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This article presents problems of unequal information importance. The paper discusses constructive methods of code generation, and a constructive method of generating asymptotic UEP codes is built. An analog model of Hamming's upper bound and Hilbert's lower bound for asymptotic UEP codes is determined.