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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
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Two applications of cyclotomic cosets to certain BCH codes (Corresp.)

IEEE Transactions on Information Theory, 1980
A more accurate designed distance bound is given for a subclass of narrow-sense primitive Bose-Chaudhuri-Hocquenghem (BCH) codes for which Mann has found the number of information digits. It is also determined when two consecutive odd integers are in the same cyclotomic coset.
D Mandelbaum
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Classes of LDPC codes constructed from elements of finite fields and cyclotomic cosets

2009 11th Canadian Workshop on Information Theory, 2009
In this paper, we derive two algebraic methods for constructing regular low density parity check (LDPC) codes - one based on elements of finite fields and the other directly based on cyclotomic cosets. We show that the constructed codes have high rates and are free of cycles of length four; consequently, they can be decoded using standard iterative ...
Salah A. Aly, Hussein Maza'ar
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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.
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Four classes of linear codes from cyclotomic cosets

Designs, Codes and Cryptography, 2017
The study of weight enumerators of linear codes is important for many goals -- it gives the error correcting ability of a given codes but also allows the computation of the probability of error detection and correction. In this paper the authors give four classes of linear codes from coset representatives of subgroups and cyclotomic coset families of ...
Dabin Zheng, Jingjun Bao
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Cyclotomy, cyclotomic cosets and arithmetic properties of some families in 𝔽l[x] 〈xptq−1〉

Asian-European Journal of Mathematics, 2022
Arithmetic properties of some families in [Formula: see text] and hence in [Formula: see text] are obtained by using the cyclotomic classes of order 2 with respect to [Formula: see text], where [Formula: see text] is primitive root modulo [Formula: see text], [Formula: see text] and [Formula: see text].
Kapil Kumar, Sudhir Batra
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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 ...
Dian-Wu Yue, Guang-Zeng Feng
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Cyclotomic cosets and steady state solutions to a dynamic jamming game

Proceedings of 1995 IEEE International Symposium on Information Theory, 2002
For an on-off slotted dynamic jamming game, a relation between the steady state solutions and cyclotomic cosets is established.
R.K. Mallik, R.A. Scholtz
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l -Cyclotomic cosets of length 2n p1α1 p2α2 p3α3

SK International Journal of Multidisciplinary Research Hub
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Construction of short binary QC-LDPC codes: Cyclotomic coset approach

2012 IEEE 11th International Conference on Signal Processing, 2012
A class of short binary (3, ρ)-regular quasi-cyclic low-density parity-check (QC-LDPC) code called cyclotomic coset (CC) code is constructed on the basis of cyclotomic coset. The length of the CC codes is less than 200 bits. The CC codes perform reasonably well over the additive white Gaussian noise (AWGN) channel with iterative decoding in terms of ...
Yanjing Zhang, Lijun Zhang
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