Coset distribution of triple-error-correcting binary primitive BCH codes

Binary primitive triple-error-correcting BCH codes have been the object of intensive studies for several decades. In the 1970s their covering radius were determined in a series of papers to be 5. However, one problem for these codes that has been open up to now is to find their coset distribution. In this paper we solve this problem and thus determine the number of cosets of each weight in binary primitive triple-error-correcting BCH codes. As a consequence this also gives the coset distribution of the extended codes with minimal distance 8