Good Codes From Generalised Algebraic Geometry Codes
Mubarak Jibril, Martin tomlinson, Mohammed Zaki Ahmed, Cen Tjhai
TL;DR
This paper introduces 41 new generalized algebraic geometry codes over GF(16) that outperform existing codes of similar length and rate, utilizing a technique involving places of small degree.
Contribution
It presents a novel construction method for generalized algebraic geometry codes using places of higher degree, improving code parameters over previous best known codes.
Findings
41 new codes over GF(16) with better performance
Utilization of small degree places in code construction
Improved code parameters compared to existing codes
Abstract
Algebraic geometry codes or Goppa codes are defined with places of degree one. In constructing generalised algebraic geometry codes places of higher degree are used. In this paper we present 41 new codes over GF(16) which improve on the best known codes of the same length and rate. The construction method uses places of small degree with a technique originally published over 10 years ago for the construction of generalised algebraic geometry codes.
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