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LIFTS OF THE TERNARY QUADRATIC RESIDUE CODE OF LENGTH 24 AND THEIR WEIGHT ENUMERATORS

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We study the extended quadratic residue code of length 24 over $\mathbb{Z}_3$ and its lifts to rings $\mathbb{Z}_{3^e}$ for all e including 3-adic integers ring. We completely determine the weight enumerators of all these lifts.

Abstract

We study the extended quadratic residue code of length 24 over $\mathbb{Z}_3$ and its lifts to rings $\mathbb{Z}_{3^e}$ for all e including 3-adic integers ring. We completely determine the weight enumerators of all these lifts.

참고문헌 (15)

  1. A.R. Calderbank, "Modular and p-adic and cyclic codes", DCC, 6, pp.21~35 (1995)
  2. S.T. Dougherty, "Lifted codes and their weight enumer- ators", Discrite Math, 305, pp.123~135 (2005)
  3. S.T. Dougherty, "Codes over the p-adic integers", Des. Codes. Cryptogr, 39, pp.65~80 (2006)
  4. S. Han, "On the weight enumerators of the projections of the 2-adic Golay codes of length 24" (2012)
  5. W.C. Human, "Fundamentals of error-correcting codes" (2003), Cambridge
  6. S.J. Kim, "Generator polynomials of the p-adic quadratic residue codes", Kangweon-Kyungki Math. J, 13, pp.103~112 (2005)
  7. R. Lidl, "Finite Fields" (2003), Cambridge
  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. Y.H. Park, "On lifted codes and p-adic codes - their weight enumerators", KIAS international conference on coding theory and applications (2012)
  14. Y.H. Park, "Quadratic residue codes over p-adic integers and their projections to integers modulo pe, in preparation", ~ (2012)
  15. Bijan Taeri, "Quadratic residue codes over Z_9", 대한수학회지, 46(1), pp.13~30 (2009), 대한수학회

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