New Quantum Codes from Skew Constacyclic Codes Over a Class Of Non-Chain Rings Re, q
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Theoretical Physics"
DOI: 10.1007/s10773-021-04910-0
Abstract: In this paper, for q = pm (p is prime) such that q ≡ 1 (mod e), we study skew constacyclic codes over a class of non-chain rings $R_{e,q}=\mathbb {F}_{q}[u]/\langle u^{e}-1\rangle $ where m, e… read more here.
Keywords: non chain; codes class; skew constacyclic; class non ... See more keywords
Constacyclic codes over the ring $${\mathbb {F}}_q+v{\mathbb {F}}_q+v^{2}{\mathbb {F}}_q$$Fq+vFq+v2Fq and their applications of constructing new non-binary quantum codes
Sign Up to like & getrecommendations! Published in 2018 at "Quantum Information Processing"
DOI: 10.1007/s11128-018-1898-6
Abstract: Let $$R={\mathbb {F}}_q+v{\mathbb {F}}_q+v^{2}{\mathbb {F}}_q$$R=Fq+vFq+v2Fq be a finite non-chain ring, where q is an odd prime power and $$v^3=v$$v3=v. In this paper, we propose two methods of constructing quantum codes from $$(\alpha +\beta v+\gamma v^{2})$$(α+βv+γv2)-constacyclic… read more here.
Keywords: mathbb vfq; quantum codes; mathbb mathbb; mathbb ... See more keywords
Application of constacyclic codes to entanglement-assisted quantum maximum distance separable codes
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DOI: 10.1007/s11128-018-1978-7
Abstract: The entanglement-assisted stabilizer formalism overcomes the dual-containing constraint of standard stabilizer formalism for constructing quantum codes. This allows ones to construct entanglement-assisted quantum error-correcting codes (EAQECCs) from arbitrary linear codes by pre-shared entanglement between the… read more here.
Keywords: assisted quantum; distance; entanglement assisted; constacyclic codes ... See more keywords
Quantum MDS codes from BCH constacyclic codes
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DOI: 10.1007/s11128-018-2049-9
Abstract: One central theme in quantum error correction is to construct quantum codes that have large minimum distances. It has been a great challenge to construct new quantum maximum-distance-separable (MDS) codes. Recently, some quantum MDS codes… read more here.
Keywords: mds codes; quantum mds; constacyclic codes; codes bch ... See more keywords
Nonbinary quantum codes from constacyclic codes over polynomial residue rings
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DOI: 10.1007/s11128-020-2584-z
Abstract: Let R be the polynomial residue ring $${\mathbb {F}}_{q^{2}}+u{\mathbb {F}}_{q^{2}}$$ F q 2 + u F q 2 , where $${\mathbb {F}}_{q^2}$$ F q 2 is the finite field with $$q^2$$ q 2 elements, q… read more here.
Keywords: quantum codes; mathbb mathbb; polynomial residue; mathbb ... See more keywords
Polyadic constacyclic codes over a non-chain ring $$\mathbb {F}_{q}[u,v]/\langle f(u),g(v), uv-vu\rangle $$
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Applied Mathematics and Computing"
DOI: 10.1007/s12190-019-01290-x
Abstract: Let f(u) and g(v) be two polynomials, not both linear, which split into distinct linear factors over \(\mathbb {F}_{q}\). Let \(\mathcal {R}=\mathbb {F}_{q}[u,v]/ \langle f(u),g(v),uv-vu\rangle \) be a finite commutative non-chain ring. In this paper,… read more here.
Keywords: non chain; langle rangle; constacyclic codes; mathbb langle ... See more keywords
Skew Constacyclic Codes over a Non-Chain Ring
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DOI: 10.3390/e25030525
Abstract: In this paper, we investigate the algebraic structure of the non-local ring Rq=Fq[v]/〈v2+1〉 and identify the automorphisms of this ring to study the algebraic structure of the skew constacyclic codes and their duals over this… read more here.
Keywords: skew constacyclic; codes non; non chain; entanglement ... See more keywords