Displaying similar documents to “Classification of Maximal Optical Orthogonal Codes of Weight 3 and Small Lengths”

On the Weight Distribution of the Coset Leaders of Constacyclic Codes

Velikova, Evgeniya, Bojilov, Asen (2008)

Serdica Journal of Computing

Similarity:

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...

Ternary constant weight codes.

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

The Electronic Journal of Combinatorics [electronic only]

Similarity:

On the Error-Correcting Performance of some Binary and Ternary Linear Codes

Baicheva, Tsonka (2007)

Serdica Journal of Computing

Similarity:

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...

Divisible Codes - A Survey

Ward, Harold (2001)

Serdica Mathematical Journal

Similarity:

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.

Maximal circular codes maximal codes

Yannick Guesnet (2010)

RAIRO - Theoretical Informatics and Applications

Similarity:

We answer to a question of De Luca and Restivo whether there exists a circular code which is maximal as circular code and not as code.

Monomial codes seen as invariant subspaces

María Isabel García-Planas, Dolors Maria Magret, Laurence Emilie Um (2017)

Open Mathematics

Similarity:

It is well known that cyclic codes are very useful because of their applications, since they are not computationally expensive and encoding can be easily implemented. The relationship between cyclic codes and invariant subspaces is also well known. In this paper a generalization of this relationship is presented between monomial codes over a finite field 𝔽 and hyperinvariant subspaces of 𝔽n under an appropriate linear transformation. Using techniques of Linear Algebra it is possible...

On Multiple Deletion Codes

Landjev, Ivan, Haralambiev, Kristiyan (2007)

Serdica Journal of Computing

Similarity:

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 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

Similarity:

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 Bounds for the Maximum Size of Ternary Constant Weight Codes

Bogdanova, Galina (2000)

Serdica Mathematical Journal

Similarity:

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.

Improvements on the Juxtaposing Theorem

Gashkov, Igor, Larsson, Henrik (2007)

Serdica Journal of Computing

Similarity:

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.

On a complete set of operations for factorizing codes

Clelia De Felice (2006)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Similarity:

It is known that the class of factorizing codes, i.e., codes satisfying the factorization conjecture formulated by Schützenberger, is closed under two operations: the classical composition of codes and substitution of codes. A natural question which arises is whether a finite set 𝒪 of operations exists such that each factorizing code can be obtained by using the operations in 𝒪 and starting with prefix or suffix codes. 𝒪 is named here a complete set of operations (for factorizing codes)....