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Seven new champion linear codes

Part of:Polytopes and polyhedraSpecial varietiesArithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  01 January 2013

Gavin Brown and
Alexander M. Kasprzyk
Gavin Brown
Affiliation:
Department of Mathematical Sciences,Loughborough University,Loughborough, LE11 3TU,United Kingdom email G.D.Brown@lboro.ac.uk
Alexander M. Kasprzyk
Affiliation:
Department of Mathematics,Imperial College London,London, SW7 2AZ,United Kingdom email a.m.kasprzyk@imperial.ac.uk

Abstract

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We exhibit seven linear codes exceeding the current best known minimum distance $d$ for their dimension $k$ and block length $n$ . Each code is defined over ${ \mathbb{F} }_{8} $ , and their invariants $[n, k, d] $ are given by $[49, 13, 27] $ , $[49, 14, 26] $ , $[49, 16, 24] $ , $[49, 17, 23] $ , $[49, 19, 21] $ , $[49, 25, 16] $ and $[49, 26, 15] $ . Our method includes an exhaustive search of all monomial evaluation codes generated by points in the $[0, 5] \times [0, 5] $ lattice square.

MSC classification

Secondary:14G50: Applications to coding theory and cryptography52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry)14M25: Toric varieties, Newton polyhedra

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 16 , October 2013, pp. 109 - 117
Copyright
© The Author(s) 2013 

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