논문KCI 등재
Cyclic codes over the ring of 4-adic integers of lengths 15, 17 and 19
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
We present a new way of obtaining the complete factorization of $X^{n}-1$ for $n=15,17,19$ over the $4$-adic ring $\O_4[X]$ of integers and thus over the Galois rings $GR(2^e,2)$. As a result, we determine all cyclic codes of lengths 15, 17 and 19 over those rings. This extends our previous work on such cyclic codes of odd lengths less than 15.
Abstract
We present a new way of obtaining the complete factorization of $X^{n}-1$ for $n=15,17,19$ over the $4$-adic ring $\O_4[X]$ of integers and thus over the Galois rings $GR(2^e,2)$. As a result, we determine all cyclic codes of lengths 15, 17 and 19 over those rings. This extends our previous work on such cyclic codes of odd lengths less than 15.
참고문헌 (10)
- A. R. Calderbank, "Modular and p-adic cyclic codes", Des. Codes. Cryptogr, 6, pp.21~35 (1995)
- S.T. Dougherty, "Lifted codes and their weight enumer-ators", Discrete Math, 305, pp.123~135 (2005)
- S.T. Dougherty, "Codes over the p-adic integers", Des. Codes. Cryptogr, 39, pp.65~80 (2006)
- F. Q. Gouvea, "p-adic numbers, An introduction" (2003), Springer
- W.C. Huffman, "Fundamentals of error-correcting codes" (2003)
- Wieb Bosma, "The Magma algebra sys-tem. I. The user language", J. Symbolic Comput, 24, pp.235~265 (1997)
- F.J. MacWilliams, "The theory of error-correcting codes" (1977), North-Holland
- Y.H. Park, "Modular independence and generator matrices for codes over Zm", Des. Codes. Cryptogr, 50, pp.147~162 (2009)
- 박영호, "The $q$-adic liftings of codes over finite fields", 한국수학논문집, 26(3), pp.537~544 (2018), 강원경기수학회
- J.-P. Serre, "Course in arithmetic" (1973), Springer
관련 논문AI추천
The $q$-adic liftings of codes over finite fields박영호강원경기수학회 · 한국수학논문집2018 · 제26권 제3호Cyclic codes over some special ringsCristina Flaut대한수학회 · 대한수학회보2013 · 제50권 제5호Quadratic residue codes over Galois rings박영호강원경기수학회 · 한국수학논문집2016 · 제24권 제3호CYCLIC CODES OF LENGTH ps OVER Fpm[u] ⟨ue⟩Karim Samei, Masoumeh Mohebbei, Rashid Rezaei, Roghayeh Mohammadi Hesari대한수학회 · 대한수학회논문집2024 · 제39권 제1호On the idempotents of cyclic codes over $\mathbb{F}_{2^t}$한성휴강원경기수학회 · 한국수학논문집2022 · 제30권 제4호Quadratic residue codes over $p$-adic integers and their projections to integers modulo $p^e$박영호강원경기수학회 · 한국수학논문집2015 · 제23권 제1호
이 간행물의 다른 논문 (17건)
On strong metric dimension of zero-divisor graphs of ringsM. Imran Bhat, SHARIEFUDDIN PIRZADApp. 563-580Some applications for generalized fractional operators in analytic functions spacesAdem Kilicman, Zainab E. Abdulnabypp. 581-594$\beta$-fuzzy filters in MS-algebrasBerhanu Assaye Alaba, Teferi Getachew Alemayehupp. 595-612Edge Szeged indices of Benzene ringMuhammad Mushtaq, Abdul Qudair Baig, Wei Gao, Muhammad Naeempp. 613-627Common fixed point results for non-compatible R-weakly commuting mappings in probabilistic semimetric spaces using control functionsKrishnapada Daspp. 629-643