Korean Journal of Mathematics

  • 제26권3호
  • /
  • Pages.537-544
  • /
  • 2018
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

THE q-ADIC LIFTINGS OF CODES OVER FINITE FIELDS

  • 투고 : 2018.08.06
  • 심사 : 2018.09.12
  • 발행 : 2018.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

There is a standard construction of lifting cyclic codes over the prime finite field ${\mathbb{Z}}_p$ to the rings ${\mathbb{Z}}_{p^e}$ 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 ${\mathbb{F}}_{p^r}$ to codes over Galois rings GR($p^e$, r). We give concrete examples with all of the lifts.

키워드

참고문헌

  1. A.R.Calderbank and N.J.A. Sloane, Modular and p-adic cyclic codes, Des. Codes. Cryptogr. 6 (1995), 21-35. https://doi.org/10.1007/BF01390768
  2. S.T. Dougherty, S.Y. Kim and Y.H. Park, Lifted codes and their weight enumerators, Discrete Math. 305 (2005), 123-135. https://doi.org/10.1016/j.disc.2005.08.004
  3. S.T. Dougherty and Y.H. Park, Codes over the p-adic integers, Des. Codes. Cryptogr. 39 (2006), 65-80. https://doi.org/10.1007/s10623-005-2542-x
  4. F. Q. Gouvea, p-adic numbers. An introduction, Springer, 2003.
  5. W.C. Huffman and V. Pless, Fundamentals of error-correcting codes, Cambridge, 2003.
  6. F.J. MacWilliams and N.J.A. Sloane, The theory of error-correcting codes, North-Holland, Amsterdam, 1977.
  7. Y.H. Park, Modular independence and generator matrices for codes over $\mathbb{Z}_m$, Des. Codes. Cryptogr. 50 (2009), 147-162. https://doi.org/10.1007/s10623-008-9220-8