On sets of vectors of a finite vector space in which every subset of basis size is a basis II

On sets of vectors of a finite vector space in which every subset of basis size is a basis II

This article contains a proof of the MDS conjecture for k ≤ 2 p − 2. That is, that if S is a set of vectors of in which every subset of S of size k is a basis, where q  =  p h , p is prime and q is not and k ≤ 2 p − 2, then | S | ≤ q  + 1. It also contains a short proof of the same fact for k  ≤ p ,...

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Veröffentlicht in:Designs, codes, and cryptography codes, and cryptography, 2012-10, Vol.65 (1-2), p.5-14
Hauptverfasser: Ball, Simeon, De Beule, Jan
Format: Artikel
Sprache:eng
Schlagworte:
Circuits
Coding and Information Theory
Computer Science
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Grafs, Teoria de
Graph theory
Information and Communication
linear codes
Matemàtiques i estadística
MDS conjecture
Singleton bound
Àrees temàtiques de la UPC
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Zusammenfassung:This article contains a proof of the MDS conjecture for k ≤ 2 p − 2. That is, that if S is a set of vectors of in which every subset of S of size k is a basis, where q  =  p h , p is prime and q is not and k ≤ 2 p − 2, then | S | ≤ q  + 1. It also contains a short proof of the same fact for k  ≤ p , for all q .
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-012-9658-6