Results 91 to 100 of about 2,328 (103)

Minimum cyclotomic coset representatives and their applications to BCH codes and Goppa codes

IEEE Transactions on Information Theory, 2000
Summary: We consider the minimum cyclotomic coset representatives and derive some of their properties. The results allow more precise estimates of the dimension of Bose-Chaudhuri-Hocquenghem (BCH) and classical Goppa codes of a given designed minimum distance, and more precise estimates of the true designed distance of BCH codes and the minimum ...
Yue, Dian-Wu, Feng, Guang-Zeng
openaire   +1 more source

Using Hash Table and Cyclotomic Coset Method for Decoding the Quadratic Residue Code

2018 IEEE International Conference on Consumer Electronics-Taiwan (ICCE-TW), 2018
A method for decoding of the quadratic residue (QR) code with hash tables is presented. The method can be applied in decoding the (31, 16, 7) QR code that the generator polynomial can be factored. In other words, the mapping between elements of syndrome $\mathbf{S}_{1}$ and all correctable error patterns is not one-to-one.
Yan-Haw Chen, C. D. Lee, J. J. Wang, Z. W. Kang   +3 more
openaire   +1 more source

Binary Locally Recoverable Codes Based on Matrices Derived from Cyclotomic Cosets

2023
A binary (n, k,r) locally recoverable code is a binary code of length n and dimension k over finite field F_2 such that a symbol in any coordinate of a codeword can be recovered by accessing the symbols in at most r other coordinates.These codes are used in distributed storage systems by Microsoft Azure and Hadoop today thanks to they can recover a ...
Zengin, Rabia, Köroğlu, Mehmet Emin
openaire   +1 more source

Cyclotomic cosets and group algebra codes define over cyclic groups of prime order

AIP Conference Proceedings, 2015
Explicit formula for all primitive idempotents in F[G], the group algebra defined over all cyclic groups G of order less than or equal to 100 over the binary field F = F2 are obtained. The minimum distance, the dimension, and the generating polynomial of the minimal codes generated by the primitive idempotents are also obtained.
openaire   +1 more source

l--Cyclotomic cosets of length 2np1α1p2α2

SK International Journal of Multidisciplinary Research Hub, 2023
openaire   +1 more source

Cyclotomic Cosets in the Ring R8pn = GF(l)[x]/(x8pn -1)

International Journal of Mathematics Trends and Technology, 2022
openaire   +1 more source

On Hard and Soft Decision Decoding of BCH Codes

IEEE Transactions on Information Theory, 2022
Martin Bossert, Rebekka Schulz, Sebastian Bitzer   +2 more
exaly  

Cyclotomic Cosets in the Ring R2pnq = GF(l)[x] / (x2pnq - 1) (n>=1)

International Journal of Mathematics Trends and Technology, 2022
openaire   +1 more source

Cyclotomic numbers and primitive idempotents in the ring GF(q)[x]/(xpn−1)

Finite Fields and Their Applications, 2004
Anuradha Sharma, Gurmeet K Bakshi, Madhu Raka   +2 more
exaly  

Existence results for cyclotomic orthomorphisms

Journal of Algebraic Combinatorics, 2017
Ian Wanless
exaly