Results 1 to 10 of about 159,782 (296)

Entanglement-Assisted Quantum Codes from Cyclic Codes [PDF]

Entropy, 2022
Entanglement-assisted quantum-error-correcting (EAQEC) codes are quantum codes which use entanglement as a resource. These codes can provide better error correction than the (entanglement unassisted) codes derived from the traditional stabilizer ...
Francisco Revson F. Pereira, Stefano Mancini   +1 more
doaj   +2 more sources

Quasi-cyclic subcodes of cyclic codes [PDF]

SIAM Journal on Discrete Mathematics, 2016
We completely characterize possible indices of quasi-cyclic subcodes in a cyclic code for a very broad class of cyclic codes. We present enumeration results for quasi-cyclic subcodes of a fixed index and show that the problem of enumeration is equivalent
Belfiore, Jean-Claude, Güneri, Cem, Özkaya, Buket   +2 more
core   +8 more sources

Cyclic Orbit Codes [PDF]

IEEE Transactions on Information Theory, 2011
In network coding a constant dimension code consists of a set of k-dimensional subspaces of F_q^n. Orbit codes are constant dimension codes which are defined as orbits of a subgroup of the general linear group, acting on the set of all subspaces of F_q^n.
Braun, Michael, Manganiello, Felice, Rosenthal, Joachim, Trautmann, Anna-Lena   +3 more
core   +4 more sources

On Quasi-Cyclic Codes of Index 3 [PDF]

Entropy
Quasi-cyclic codes of index 3 over finite fields are studied. We give a classification of such codes. Their duals with respect to the Euclidean and Hermitian inner products are investigated.
Kanat Abdukhalikov, Rasha M. Shat
doaj   +2 more sources

Skew Cyclic Codes Over ℤ₄ + uℤ₄ With Derivation Based on a New Gray Map and Automorphism

IEEE Access
This paper investigates the algebraic structure and properties of skew cyclic codes over the finite chain ring $R = \mathbb {Z}_{4} + u\mathbb {Z}_{4}$ , where $u^{2} = 0$ .
Eda Tekin
doaj   +2 more sources

Cyclic Sieving for cyclic codes [PDF]

Finite Fields and Their Applications, 2021
Prompted by a question of Jim Propp, this paper examines the cyclic sieving phenomenon (CSP) in certain cyclic codes. For example, it is shown that, among dual Hamming codes over $F_q$, the generating function for codedwords according to the major index statistic (resp. the inversion statistic) gives rise to a CSP when $q=2$ or $q=3$ (resp. when $q=2$).
Mason, Alex, Reiner, Victor, Sridhar, Shruthi   +2 more
openaire   +2 more sources

A NEW CLASS OF ISODUAL CYCLIC CODES OF RATE 1/2 OVER F_p [PDF]

Romanian Journal of Mathematics and Computer Science, 2016
A new class of isodual cyclic codes of parameters [n, k]_p, is found for n singly even, not a multiple of ...
CHERIF MIHOUBI, PATRICK SOLE
doaj   +1 more source

Inverse Quasi-Cyclic Codes and Automorphism Cyclic Codes

International Journal of Advanced Natural Sciences and Engineering Researches, 2023
Mustafa ÖZKAN
openaire   +3 more sources

On skew cyclic codes over $ M_{2}(\mathbb{F}_{2}) $

AIMS Mathematics, 2023
The algebraic structure of skew cyclic codes over $ M_{2} $($ \mathbb{F}_2 $), using the $ \mathbb{F}_4 $-cyclic algebra, is studied in this work. We determine that a skew cyclic code with a polynomial of minimum degree $ d(x) $ is a free code generated ...
Xuesong Si, Chuanze Niu
doaj   +1 more source

New DNA Codes from Cyclic Codes over Mixed Alphabets

Mathematics, 2020
Let R=F4+uF4,withu2=u and S=F4+uF4+vF4,withu2=u,v2=v,uv=vu=0. In this paper, we study F4RS-cyclic codes of block length (α,β,γ) and construct cyclic DNA codes from them. F4RS-cyclic codes can be viewed as S[x]-submodules of Fq[x]〈xα−1〉×R[x]〈xβ−1〉×S[x]〈xγ−
Hai Q. Dinh, Sachin Pathak, Ashish Kumar Upadhyay, Woraphon Yamaka   +3 more
doaj   +1 more source