Minimal quadratic residue cyclic codes of lengthp n(p odd prime)

• DOI: 10.1007/bf02941985
• Publication Date: 2019-09-27T03:20:47Z
• Authors: Sudhir Batra; S. K. Arora
• Keywords: 0202 electrical engineering, electronic engineering, information engineering; 02 engineering and technology

The explicit expressions for the 2n + 1 primitive idempotents in\(R_{p^ - } = F[x]/ \), whereF is the field of prime power orderq and the multiplicative order ofq modulopn is ϕ(pn)/2 (n ≥ 1 andp is an odd prime), are obtained. An algorithm for computing the generating polynomials of the minimal QR cyclic codes of lengthpn, generated by these primitive idempotents, is given and hence some bounds on the minimum distance of some QR codes of prime length overGF(q)(q = 2, 3, ...) are obtained.