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n -T-quasigroup codes with one check symbol and their error detection capabilities

Gary L. Mullen, Viktor Alekseevich Shcherbakov (2004)

Commentationes Mathematicae Universitatis Carolinae

It is well known that there exist some types of the most frequent errors made by human operators during transmission of data which it is possible to detect using a code with one check symbol. We prove that there does not exist an n -T-code that can detect all single, adjacent transposition, jump transposition, twin, jump twin and phonetic errors over an alphabet that contains 0 and 1. Systems that detect all single, adjacent transposition, jump transposition, twin, jump twin errors and almost all...

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

Dontcheva, Radinka (2001)

Serdica Mathematical Journal

∗ This work was supported in part by the Bulgarian NSF under Grant MM-901/99In 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.

New Bounds for the Maximum Size of Ternary Constant Weight Codes

Bogdanova, Galina (2000)

Serdica Mathematical Journal

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.

New Upper Bounds for Some Spherical Codes

Boyvalenkov, Peter, Kazakov, Peter (1995)

Serdica Mathematical Journal

The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases...

Nonassociative algebras: some applications.

Santos González, Consuelo Martínez (2003)

Revista Matemática Iberoamericana

Nonassociative algebras can be applied, either directly or using their particular methods, to many other branches of Mathematics and other Sciences. Here emphasis will be given to two concrete applications of nonassociative algebras. In the first one, an application to group theory in the line of the Restricted Burnside Problem will be considered. The second one opens a door to some applications of non-associative algebras to Error correcting Codes and Cryptography.

Note on an Improvement of the Griesmer Bound for q-ary Linear Codes

Hamada, Noboru, Maruta, Tatsuya (2011)

Serdica Journal of Computing

Let nq(k, d) denote the smallest value of n for which an [n, k, d]q code exists for given integers k and d with k ≥ 3, 1 ≤ d ≤ q^(k−1) and a prime or a prime power q. The purpose of this note is to show that there exists a series of the functions h3,q, h4,q, ..., hk,q such that nq(k, d) can be expressed.This research was partially supported by Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science under Contract Number 20540129.

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