The Coset Distribution of Triple-Error-Correcting
Binary 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.