Gashkov, Igor, Larsson, Henrik (2007)
Serdica Journal of Computing
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A new class of binary constant weight codes is presented. We establish new lower bound and exact values on A(n1 +n2; 2(a1 +a2); n2) ≥ min {M1;M2}+1, if A(n1; 2a1; a1 +b1) = M1 and A(n2; 2b2; a2 +b2) = M2, in particular, A(30; 16; 15) = 16 and A(33; 18; 15) = 11.
Bogdanova, Galina (2000)
Serdica Mathematical Journal
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This work was partially supported by the Bulgarian National Science Fund under Grant I–618/96. Optimal ternary constant-weight lexicogarphic codes have been constructed. New bounds for the maximum size of ternary constant-weight codes are obtained. Tables of bounds on A3 (n, d, w) are given for d = 3, 4, 6.
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...
Gashkov, I., Taub, D. (2007)
The Electronic Journal of Combinatorics [electronic only]
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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.
King, Oliver D. (2003)
The Electronic Journal of Combinatorics [electronic only]
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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.
Manev, Mladen (2009)
Serdica Journal of Computing
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Partially supported by the Technical University of Gabrovo under Grant C-801/2008 One of the main problems in the theory of superimposed codes is to find the minimum length N for which an (N, T,w, r) superimposed code exists for given values of T , w and r. Let N(T,w, r) be the minimum length N for which an (N, T,w, r) superimposed code exists. The (N, T,w, r) superimposed code is called optimal when N = N(T,w, r). The values of N(T, 1, 2) are known for T ≤ 12 and the values...
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...
Dontcheva, Radinka (2001)
Serdica Mathematical Journal
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∗ This work was supported in part by the Bulgarian NSF under Grant MM-901/99 In this paper we prove that up to equivalence there exist 158 binary [70, 35, 12] self-dual and 119 binary [72, 36, 12] self-dual doubly-even codes all of which have an automorphism of order 23 and we present their construction. All these codes are new.
Baicheva, Tsonka (2007)
Serdica Journal of Computing
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In this work, we determine the coset weight spectra of all binary cyclic codes of lengths up to 33, ternary cyclic and negacyclic codes of lengths up to 20 and of some binary linear codes of lengths up to 33 which are distance-optimal, by using some of the algebraic properties of the codes and a computer assisted search. Having these weight spectra the monotony of the function of the undetected error probability after t-error correction P(t)ue (C,p) could be checked with any precision...