Open AccessSome new codes from binary Goppa codes and a method of shortening linear codes
Author(s) -
Jibril Mubarak,
Tomlinson Martin,
Tjhai Cen Jung,
Ahmed Mohammed Zaki,
Bezzateev Sergey
Publication year - 2013
Publication title -
iet communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.355
H-Index - 62
eISSN - 1751-8636
pISSN - 1751-8628
DOI - 10.1049/iet-com.2011.0693
Subject(s) - linear code , concatenated error correction code , block code , mathematics , reed–muller code , code (set theory) , low density parity check code , raptor code , expander code , binary number , discrete mathematics , algorithm , computer science , decoding methods , arithmetic , programming language , set (abstract data type)
Goppa codes have some of the largest minimum distances possible for linear codes. The authors use some binary Goppa codes in which four new binary codes are obtained with parameters better than any codes known to date. The authors also present the necessary conditions for a code obtained by shortening a longer code which will have a greater minimum distance than the original code.