Results on binary cyclic codes |
Thirty-seven binary cyclic codes with minimum distance higher than those of the best linear codes given in Brouwer's table are presented. Among these new cyclic codes is the quadratic residue code of length 199, for which is provided an answer to the long-open question regarding its minimum distance. Four new binary linear codes are also obtained by applying Construction X and Construction Y1 to those new cyclic codes. Overall, after taking into account the extended, punctured and shortened codes, there are 869 binary linear codes which are improvements to Brouwer's lower-bound.
Tjhai CJ, Tomlinson M