Results 51 to 60 of about 2,432,274 (184)

Quantum MDS Codes over Small Fields

, 2015
We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$ with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic codes, new QMDS codes can be ...
Grassl, Markus, Roetteler, Martin
core   +1 more source

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

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   +1 more source

On Gray Images of Constacyclic Codes

ITM Web of Conferences, 2018
This paper deals with constacyclic codes over a new ring. Gray images of these codes over those rings are obtained. The relations between these codes and their Gray images are given.
Özkan Mustafa, Öke Figen
doaj   +1 more source

Non-binary quantum codes from constacyclic codes over 𝔽q[u1, u2,…,uk]/⟨ui3 = ui, uiuj = ujui⟩

Open Mathematics, 2022
Let q=pmq={p}^{m}, pp be an odd prime, and Rk=Fq[u1,u2,…,uk]/⟨ui3=ui,uiuj=ujui⟩{R}_{k}={{\mathbb{F}}}_{q}\left[{u}_{1},{u}_{2},\ldots ,{u}_{k}]\hspace{-0.08em}\text{/}\hspace{-0.08em}\langle {u}_{i}^{3}={u}_{i},{u}_{i}{u}_{j}={u}_{j}{u}_{i}\rangle ...
Kong Bo, Zheng Xiying
doaj   +1 more source

Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes

, 2012
Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring.
Lopez-Permouth, Sergio R., Ozadam, Hakan, Ozbudak, Ferruh, Szabo, Steve   +3 more
core   +1 more source

Isodual constacyclic codes

Finite Fields and Their Applications, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Symbol-Triple Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over ${\mathbb{F}}_q+u{\mathbb{F}}_q+u^2{\mathbb{F}}_q$

Mathematics, 2022
Let p be an odd prime, where ϑ and m are positive integers. Let ψ be a nonzero element of the finite field Fq, where q=pm, and R=Fq+uFq+u2Fq(u3=0). In this paper, we determine completely the symbol-triple distances of all ψ-constacyclic codes of length ...
Hai Q. Dinh, Jamal Laaouine, Brahim Boudine, Woraphon Yamaka   +3 more
doaj   +1 more source

Symbol-Pair Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over \({{\mathbb{F}_{p^m}[u]}/{\langle u^3\rangle}}\)

Mathematics, 2021
Let p be a prime, s, m be positive integers, γ be a nonzero element of the finite field Fpm, and let R=Fpm[u]/⟨u3⟩ be the finite commutative chain ring.
Mohammed E. Charkani, Hai Q. Dinh, Jamal Laaouine, Woraphon Yamaka   +3 more
doaj   +1 more source

On Linear Perfect b-Symbol Codes over Finite Fields

Mathematics, 2023
Motivated by the application of high-density data storage technologies, Cassuto and Blaum introduced codes for symbol-pair read channels in 2011, and Yaakobi et al. generalized the coding framework to that for b-symbol read channels where b≥2 in 2016. In
Kanat Abdukhalikov, Jiajie Chen, Rongquan Feng   +2 more
doaj   +1 more source

On optimal constacyclic codes

Linear Algebra and its Applications, 2016
In this paper we investigate the class of constacyclic codes, which is a natural generalization of the class of cyclic and negacyclic codes. This class of codes is interesting in the sense that it contains codes with good or even optimal parameters.
openaire   +3 more sources