CYCLIC CODES ASSOCIATED TO MUFFIN IDEALS OVER QUATERNION INTEGER RING (-1,-1)/zp )
SHAIKH JAVED SHAFEE *
Government Polytechnic, Hingoli, Maharashtra, India.
ARUNKUMAR R. PATIL
Department of Mathematics, Shri Guru Gobind Singhji Institute of Engineering and Technology, Vishnupuri, Nanded, Maharashtra, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we construct cyclic codes associated with Muffin ideals over quaternion integer rings-(-1,-1/zp ), where zp is the finite field integers modulo odd prime p. We also find a generator matrix in standard form for these cyclic codes. Further we determine the Mannheim distance of these cyclic codes.
Keywords: Cyclic codes, Quaternion algebra, muffin ideal, Mannheim distance