A Characterization of the Codes over Fp
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A new Gray map between codes over Fp+uFp+u2Fp+u3Fp and codes over Fp is de¯ned. It is proved that the Gray image of the linear (1 - u3)-cyclic code over the commutative ring Fp + uFp + u2Fp + u3Fp of length n is a distance invariant quasicyclic code of index p2 and the length p3n over Fp. And it is proved that if (n,p) = 1, then every code over Fp which is the Gray image of a linear cyclic code over Fp + uFp + u2Fp + u3Fp of length n is permutation equivalent to a quasi-cyclic code of index p2.
Abstract
A new Gray map between codes over Fp+uFp+u2Fp+u3Fp and codes over Fp is de¯ned. It is proved that the Gray image of the linear (1 - u3)-cyclic code over the commutative ring Fp + uFp + u2Fp + u3Fp of length n is a distance invariant quasicyclic code of index p2 and the length p3n over Fp. And it is proved that if (n,p) = 1, then every code over Fp which is the Gray image of a linear cyclic code over Fp + uFp + u2Fp + u3Fp of length n is permutation equivalent to a quasi-cyclic code of index p2.
참고문헌 (6)
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