The Coset Distribution of Triple-Error-Correcting
Primitive BCH Codes
Pascale Charpin, Tor Helleseth and Victor Zinoviev
INRIA (projet CODES), University of Bergen, and IPIT (Moscow)
France, Norway, Russia
Presented at ISIT 2005, Adelaide, Australie.
IEEE Trans. on Info. Theory, 52(4), 1727-1732, 2006.
Binary primitive triple-error-correcting BCH codes
of length $n=2^m-1$ 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 equal to 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 of length
$N=2^m$ with minimal distance 8.
Keywords : BCH codes, covering radius, coset distribution.