Title :
Results on Binary Linear Codes With Minimum Distance 8 and 10
Author :
Bouyukliev, Iliya Georgiev ; Jacobsson, Erik
Author_Institution :
Inst. of Math. & Inf., Bulgarian Acad. of Sci., Veliko Tarnovo, Bulgaria
Abstract :
All linear binary codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact bounds for binary linear codes. Primarily two algorithms considering the dual codes are used, namely extension of dual codes with a proper coordinate, and a fast algorithm for finding a maximum clique in a graph, which is modified to find a maximum set of vectors with the right dependency structure.
Keywords :
binary codes; dual codes; linear codes; set theory; vectors; binary linear code; dual code; graph theory; right dependency structure; vector set; Binary codes; Generators; Linear code; Parity check codes; Vectors; Algorithms; classification of codes; linear codes; optimal codes;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2162264
