Results 1 to 10 of about 36,705 (229)

Repeated-root cyclic codes [PDF]

IEEE Transactions on Information Theory, 1991
In the theory of cyclic codes, it is common practice to require that (n,q)=1, where n is the word length and F/sub q/ is the alphabet. It is shown that the even weight subcodes of the shortened binary Hamming codes form a sequence of repeated-root cyclic codes that are optimal.
J. H. van Lint
exaly   +5 more sources

Some Classes of New Quantum MDS and Synchronizable Codes Constructed From Repeated-Root Cyclic Codes of Length 6p^s [PDF]

IEEE Access, 2021
In this paper, we use the CSS and Steane’s constructions to establish quantum error-correcting codes (briefly, QEC codes) from cyclic codes of length $6p^{s}$ over $\mathbb F_{p^{m}}$ .
Hai Q. Dinh, Ha T. Le, Bac T. Nguyen, Paravee Maneejuk   +3 more
doaj   +3 more sources

MDS symbol-pair codes from repeated-root cyclic codes [PDF]

Designs, Codes and Cryptography, 2021
arXiv admin note: text overlap with arXiv:2010 ...
Junru Ma, Jinquan Luo
exaly   +5 more sources

On the Hamming Distance of Repeated-Root Cyclic Codes of Length 6p^s [PDF]

IEEE Access, 2020
Let $p$ be an odd prime, $s$ , $m$ be positive integers such that $p^{m}\equiv 2 \pmod 3$ . In this paper, using the relationship about Hamming distances between simple-root cyclic codes and repeated-root cyclic codes, the Hamming distance of all ...
Hai Q. Dinh, Xiaoqiang Wang, Paravee Maneejuk   +2 more
doaj   +3 more sources

A Note on Repeated-Root Cyclic Codes [PDF]

IEEE Transactions on Information Theory, 1991
In papers by Castagnoli et al. and Van Lint, cyclic codes with repeated roots are analyzed. Both papers fail to acknowledge a previous work by Chen, dating back to 1969, which includes an analysis of even, length binary cyclic codes.
Morelos-Zaragoza, Robert H
core   +7 more sources

Repeated-root cyclic and negacyclic codes over a finite chain ring [PDF]

Discrete Applied Mathematics, 2005
We show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2.
Berg, R. van den, Berkhemer, O.A., Dippel, D.W.J., Jansen, I.G.H., Lingsma, H.F., Lugt, A. van der, Majoie, C.B.L.M., Marquering, H.A., MR CLEAN Trial Investigators, Oostenbrugge, R.J. van, Roos, Y.B.W.E.M., Slump, C.H., Treurniet, K.M., Vuuren, A.B. van, Walderveen, M.A.A. van, Wijngaard, I.R. van den, Zwam, W.H. van   +16 more
core   +9 more sources

Repeated-Root Cyclic Codes with Optimal Parameters or Best Parameters Known [PDF]

Cyclic codes are the most studied subclass of linear codes and widely used in data storage and communication systems. Many cyclic codes have optimal parameters or the best parameters known. They are divided into simple-root cyclic codes and repeated-root
Chen, Hao, Ding, Cunsheng, Xie, Conghui
core   +3 more sources

On Hamming Distance Distributions of Repeated-Root Cyclic Codes of Length 5p^s Over F_p ^m + uF_p ^m [PDF]

IEEE Access, 2022
Let $p\not =5$ be any odd prime. Using the algebraic structures of all cyclic codes of length $5p^{s}$ over the finite commutative chain ring ${\mathcal{ R}}=\mathbb F_{p^{m}}+u\mathbb F_{p^{m}}$ , in this paper, the exact values of Hamming ...
Hai Q. Dinh, Bac T. Nguyen, Hiep L. Thi, Woraphon Yamaka   +3 more
doaj   +2 more sources

AMDS Symbol-Pair Codes from Repeated-Root Cyclic Codes [PDF]

, 2022
arXiv admin note: text overlap with arXiv:2010.04329.
Junru Ma
openalex   +3 more sources

Squaring Construction For Repeated-Root Cyclic Codes

, 2010
{"references": ["E. Rains and N.J.A. Sloane, \"Self-dual codes,\" in Handbook of Coding\nTheory, V.S. Pless and W.C. Huffman (Editors), Elsevier, Amsterdam,\npp. 177-294, 1998.", "J. H. Conway and V. Pless, \"On the enumeration of self-dual codes,\" J.\nCombinatorial Theory, 28A, 26-53, 1980.", "F. J. MacWilliams and N. J. A.
O.P. Vinocha, Jaskarn Singh Bhullar, Manish K. Gupta   +2 more
openalex   +3 more sources