Encoding and decoding of BCH codes using light and short codewords

R.M. Roth, G. Seroussi
1988 IEEE Transactions on Information Theory  
It is shown that every q-ary primitive BCH code of designed distance δ and sufficiently large length n contains a codeword c 0 of weight w = O(δ ), and degree deg(c 0 ) = o(n). These so called light and short codewords are used to describe encoding and decoding algorithms which run on sequential machines in time O(δ n), i.e. linear in n for fixed δ . For high-rate primitive BCH codes this is faster than the commonly used algorithms, which are nonlinear in n when run on sequential machines.
doi:10.1109/18.6045 fatcat:cwejcdjuq5hltbvgqzr6fgqcgq