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Quadratic residue codes over $p$-adic integers and their projections to integers modulo $p^e$

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초록

We give idempotent generators for quadratic residue codes over $p$-adic integers and over the rings $\Z_{p^e}$.

Abstract

We give idempotent generators for quadratic residue codes over $p$-adic integers and over the rings $\Z_{p^e}$.

참고문헌 (13)

  1. A.R. Calderbank, "Modular and p-adic and cyclic codes", DCC, 6, pp.21~35 (1995)
  2. M.H Chiu, "Z8-cyclic codes and quadratic residue codes", Advances in Algebra, 25, pp.12~33 (2000)
  3. S.T. Dougherty, "Lifted codes and their weight enumer-ators", Discrite Math, 305, pp.123~135 (2005)
  4. S.T. Dougherty, "Codes over the p-adic integers", Des. Codes. Cryptogr, 39, pp.65~80 (2006)
  5. W.C. Hu man, "Fundamentals of error-correcting codes" (2003), Cambridge
  6. S.J. Kim, "Quadratic residue codes over Z16", Kangweon-Kyungki Math. J, 11, pp.57~64 (2003)
  7. S.J. Kim, "Generator polynomials of the p-adic quadratic residue codes", Kangweon-Kyungki Math. J, 13, pp.103~112 (2005)
  8. F.J. MacWilliams, "The theory of error-correcting codes" (1977), North-Holland
  9. B.R. McDonald, "Finite rings with identity" (1974), Dekker
  10. K. Nagata, "On self-dual codes over Z16", Lecture Notes in Computer Science, 5527, pp.107~116 (2009)
  11. G. Nebe, "Self-dual codes and invariant theory" (2006), Springer-Verlag
  12. Y.H. Park, "Modular independence and generator matrices for codes over Zm", Des. Codes. Crypt, 50, pp.147~162 (2009)
  13. Bijan Taeri, "Quadratic residue codes over Z_9", 대한수학회지, 46(1), pp.13~30 (2009), 대한수학회

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