Displaying similar documents to “Information sets as permutation cycles for quadratic residue codes.”

On Binary Self-Dual Codes of Length 62 with an Automorphism of Order 7 Двоични самодуални кодове с дължина 62 притежаващи автоморфизъм от ред 7

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...

New Binary [ 70 , 35 , 12 ] Self-Dual and Binary [ 72 , 36 , 12 ] Self-Dual Doubly-Even Codes

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.

Some MDS Codes over Gf(64) Connected with the Binary Doubly-Even [72,36,16] Code

Bouyuklieva, Stefka (2007)

Serdica Journal of Computing

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* The author is supported by a Return Fellowship from the Alexander von Humboldt Foundation. MDS [8,4,5] codes over a field with 64 elements are constructed. All such codes which are self-dual under a Hermitian type inner product are classified. The connection between these codes and a putative binary self- dual [72,36,16] code is considered.

Ternary constant weight codes.

Östergård, Patric R.J., Svanström, Mattias (2002)

The Electronic Journal of Combinatorics [electronic only]

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On Extremal Binary Doubly-Even Self-Dual Codes of Length 88*

Yorgova, Radinka, At, Nuray (2009)

Serdica Journal of Computing

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In this paper we present 35 new extremal binary self-dual doubly-even codes of length 88. Their inequivalence is established by invariants. Moreover, a construction of a binary self-dual [88, 44, 16] code, having an automorphism of order 21, is given. *This work was partly supported by the Norwegian Government Scholarship.

Divisible Codes - A Survey

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.

On Multiple Deletion 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...

On the Weight Distribution of the Coset Leaders of Constacyclic Codes

Velikova, Evgeniya, Bojilov, Asen (2008)

Serdica Journal of Computing

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Constacyclic codes with one and the same generator polynomial and distinct length are considered. We give a generalization of the previous result of the first author [4] for constacyclic codes. Suitable maps between vector spaces determined by the lengths of the codes are applied. It is proven that the weight distributions of the coset leaders don’t depend on the word length, but on generator polynomials only. In particular, we prove that every constacyclic code has the same weight distribution...

Improvements on the Juxtaposing Theorem

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.