Abstract
The $m$-covering radii of codes are natural generalizations of the covering radii of codes. In this paper we analyze the 2-covering radii of double error correcting BCH code. In particular, we show that the 2-covering radius of the double error correcting BCH code is $(n+1)/2$ for sufficiently large $n$.
Highlights
Multicovering radii are generalizations of the covering radius
Given a code C of length n, the m-covering radius of C, denoted by tm(C), is the smallest natural number r such that every m-tuple of vectors in F n is contained in a ball of radius r centered around some codeword of C
We show that the 2-covering radius of the double error correcting BCH code is (n + 1)/2 for sufficiently large n
Summary
Multicovering radii are generalizations of the covering radius. Let m and n be natural numbers. Given a code C of length n, the m-covering radius of C, denoted by tm(C), is the smallest natural number r such that every m-tuple of vectors in F n is contained in a ball of radius r centered around some codeword of C. We show that the 2-covering radius of the double error correcting BCH code is (n + 1)/2 for sufficiently large n.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
