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The parity of cyclotomic numbers of order 2, 4 and 6 associated with 4-cyclotomic cosets modulo an odd prime $p$ are obtained. Hence the explicit expressions of primitive idempotents of minimal cyclic codes of length $p^{n}$, $n\ge 1$ over the quaternary field $F_{4}$ are obtained. These codes are observed to be subcodes of $Q$ codes of length $p^{n}$. Some orthogonal properties of these subcodes are discussed. The minimal cyclic codes of length 17 and 43 are also discussed and it is observed that the minimal cyclic codes of length 17 are two weight codes. Further, it is shown that a $Q$ code of prime length is always cyclotomic like a binary duadic code and it seems that there are infinitely many prime lengths for which cyclotomic $Q$ codes of order 6 exist.
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참고문헌 (30)
참고문헌 신청
S. K. Arora / 2005 / The primitive idempotents of a cyclic group algebra. II / Southeast Asian Bull. Math. 29(2):197~208
S. K. Arora / 2002 / The primitive idempotents of a cyclic group algebra / Southeast Asian Bull. Math. 26(4):549~557
S. K. Arora / 1999 / Minimal cyclic codes of length $2p^n$ / Finite Fields Appl. 5(2):177~187
G. K. Bakshi / 2002 / Minimal cyclic codes of length $2^m$ / Ranchi Univ. Math. J. 33:1~18
G. K. Bakshi / 2003 / Minimal cyclic codes of length $p^nq$ / Finite Fields Appl. 9(4):432~448
S. K. Arora / 2002 / The primitive idempotents of a cyclic group algebra / Southeast Asian Bull. Math. 26(4):549~557
S. K. Arora / 1999 / Minimal cyclic codes of length
G. K. Bakshi / 2002 / Minimal cyclic codes of length
G. K. Bakshi / 2003 / Minimal cyclic codes of length
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