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Quadratic residue codes over R = F_p + uF_p + vF_p + uvF_p + v^2 F_p + uv^2 F_p

Ramez AL-SHORBASSI, Mohammed AL-ASHKER, Gamal ISMAIL

Abstract



In this paper, we study quadratic residue codes of prime length q over the ring R = F_p + uF_p + vF_p + uvF_p + v^2 F_p + uv^2 F_p, where v^3 = v, u^2 = 1,uv = vu, and p is an odd prime. Quadratic residue codes and their extensions over R are defined. Some properties of quadratic residue codes over R are studied. A self-dual code [120; 60] over F_7, and self-dual code [108; 54] over F_13,are obtained from extended quadratic residue codes.

Keywords


Quadratic Residue Codes, Generating Idempotents, Self-Dual Codes, Gray Map.

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