Divisibility of Codes Meeting the Griesmer Bound
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It is proved that if a linear code overGF(p),pa prime, meets the Griesmer bound, then ifpedivides the minimum weight, then all word weights are won.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1998-07-01 and is currently open access. It has received 60 citations till now. The article focuses on the topics: Prime (order theory) & Divisibility rule.read more
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Journal ArticleDOI
The combinatorics of LCD codes: linear programming bound and orthogonal matrices
TL;DR: In this article, a linear programming bound on the largest size of a linear complementary dual (LCD) code of given length and minimum distance is given, and a table of lower bounds for this combinatorial function for modest values of the parameters.
Book ChapterDOI
Partial spreads and vector space partitions
TL;DR: In this paper, the authors provide a historic account on partial spreads and an interpretation of the classical results from a modern perspective, and introduce all required methods from the theory of vector space partitions and Finite Geometry in a tutorial style.
Posted Content
The combinatorics of LCD codes: Linear Programming bound and orthogonal matrices
TL;DR: In this paper, the largest size of a linear complementary dual code of given length and minimum distance is given, and a table of lower bounds for this combinatorial function for modest values of the parameters is given.
Journal Article
Divisible Codes - A Survey
TL;DR: This paper surveys parts of the study of divisibility properties of codes, including the motivating background involving polynomials over nite elds and recent results on bounds and applications to optimal codes.
Book
Current Research Topics on Galois Geometry
Leo Storme,Jan De Beule +1 more
TL;DR: In this article, the polynomial method in Galois geometries is used to construct classical sets in PG(n,q) substructures of finite classical polar spaces.
References
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A theorem on the distribution of weights in a systematic code
TL;DR: The spectrum of a systematic code determines uniquely the spectrum of its dual code (the orthogonal vector space) and the two sets of integers are related by a system of linear equations.
Journal ArticleDOI
New 5-designs
E. F. Assmus,H. F. Mattson +1 more
TL;DR: In this article, the theory of error-correcting codes has been used to construct new 5-designs on 24 and 48 points as well as the two classic 5 designs on 12 and 24 points associated with the Mathieu groups M12 and M24.
Journal ArticleDOI
Caps and codes
TL;DR: Improved general upper bounds on m ( r, q ) are found, which give m (5, 3)⩽56 as a particular case of an ovaloid in the projective space S r,q of dimension r over a field of q elements.