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There is a standard construction of lifting cyclic codes over the prime finite field $\Z_p$ to the rings $\Z_{p^e}$ and to the ring of $p$-adic integers. We generalize this construction for arbitrary finite fields. This will naturally enable us to lift codes over finite fields $\F_{p^r}$ to codes over Galois rings $GR(p^e,r)$. We give concrete examples with all of the lifts.
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참고문헌 (7)
참고문헌 신청
A.R.Calderbank / 1995 / Modular and p-adic cyclic codes / Des. Codes. Cryptogr. 6:21~35
S.T. Dougherty / 2005 / Lifted codes and their weight enumerators / Discrete Math. 305:123~135
S.T. Dougherty / 2006 / Codes over the p-adic integers / Des. Codes. Cryptogr. 39:65~80
F. Q. Gouvea / 2003 / p-adic numbers. An introduction / Springer
W.C. Huffman / 2003 / Fundamentals of error-correcting codes
S.T. Dougherty / 2005 / Lifted codes and their weight enumerators / Discrete Math. 305:123~135
S.T. Dougherty / 2006 / Codes over the p-adic integers / Des. Codes. Cryptogr. 39:65~80
F. Q. Gouvea / 2003 / p-adic numbers. An introduction / Springer
W.C. Huffman / 2003 / Fundamentals of error-correcting codes
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