Some results on improving the code length of SbEC-DED codes

The single b-bit byte error correcting and double bit error detecting (SbEC-DED) codes have important applications in computer high-speed memories. In 1992, a class of practical SbEC-DED codes was given by Fujiwara and Hamada. Their constructions are based on the existence of cosets of a subfield of GF(2^b) where the codes are defined. The code length is determined by the number of the cosets and the size of the cosets. Clearly, there is a major drawback in their constructions, that is, the constructions will fail if b is a prime since there exists no nontrivial subfield. To overcome this weakness, we present a more general construction method using subsets of GF(2^b ) instead of the cosets of a subfield of GF(2^b). By doing this, the codes obtained by Fujiwara and Hamada are special cases of our constructions and, for some b, the sets used in our construction are bigger than the cosets they used and hence a larger code length can be obtained