On the minimum distance of negacyclic codes with two zeros

Abstract We investigate the minimum distance of q-ary negacyclic codes of length q m − 1 2 generated by a product of two distinct minimal polynomials. A necessary and sufficient condition on the minimum distance of such negacyclic codes is given. Several classes of optimal quinary negacyclic codes with parameters [ ( 5 m − 1 ) / 2 , ( 5 m − 1 ) / 2 − 2 m , 4 ] are constructed. The dual codes of a subclass of the quinary negacyclic codes are studied. A comparison with cyclic codes is also presented.

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