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Binary [ n , (n + 1)/2] Cyclic Codes With Good Minimum Distances.
- Source :
-
IEEE Transactions on Information Theory . Dec2022, Vol. 68 Issue 12, p7842-7849. 8p. - Publication Year :
- 2022
-
Abstract
- The binary quadratic-residue codes and the punctured Reed-Muller codes ${\mathcal {R}}_{2}((m-1)/2, m))$ are two families of binary cyclic codes with parameters $[n, (n+1)/2, d \geq \sqrt {n}]$. These two families of binary cyclic codes are interesting partly due to the fact that their minimum distances have a square-root bound. The objective of this paper is to construct two families of binary cyclic codes of length $2^{m}-1$ and dimension near $2^{m-1}$ with good minimum distances. When $m \geq 3$ is odd, the codes become a family of duadic codes with parameters $[2^{m}-1, 2^{m-1}, d]$ , where $d \geq 2^{(m-1)/2}+1$ if $m \equiv 3 \pmod {4}$ and $d \geq 2^{(m-1)/2}+3$ if $m \equiv 1 \pmod {4}$. The two families of binary cyclic codes contain some optimal binary cyclic codes. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CYCLIC codes
*REED-Muller codes
*BINARY codes
*LINEAR codes
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 160651294
- Full Text :
- https://doi.org/10.1109/TIT.2022.3193715