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New quantum MDS code from constacyclic codes
Chinese Annals of Mathematics, Series B, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hu, Liqin, Yue, Qin, Zhu, Xiaomeng
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Optimal constacyclic locally repairable codes
IEEE Communications Letters, 2019Being part of distributed storage systems, locally repairable codes (LRCs) have drawn great attention in the past years. Inspired by a recent construction of optimal LRCs-based on cyclic codes, constacyclic LRCs are studied in this letter. Specifically, a family of optimal constacyclic $(r,\delta)_{q}$ -LRCs with unbounded length and minimum ...
Zhonghua Sun, Shixin Zhu, Liqi Wang
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Two Classes of Constacyclic Codes With Variable Parameters [(qm – 1)/r, k, d]
IEEE Transactions on Information TheoryConstacyclic codes over finite fields are a family of linear codes and contain cyclic codes as a subclass. Constacyclic codes are related to many areas of mathematics and outperform cyclic codes in several aspects.
Zhonghua Sun, C. Ding, Xiaoqiang Wang
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Some New Quantum Codes from Constacyclic BCH Codes
International Journal of Theoretical PhysicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Ping +3 more
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IEEE Transactions on Information Theory, 1994
Summary: A class of \(q^ m\)-ary constacyclic codes is defined which has the property that the \(q\)-ary image is equivalent to a class of shortened cyclic codes. This description leads to the construction of nonlinear codes. As an example one can construct nonlinear codes of length \(N= q^ m+1\) over the field \(\text{GF} (q^{m'})\), \(m'\leq m ...
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Summary: A class of \(q^ m\)-ary constacyclic codes is defined which has the property that the \(q\)-ary image is equivalent to a class of shortened cyclic codes. This description leads to the construction of nonlinear codes. As an example one can construct nonlinear codes of length \(N= q^ m+1\) over the field \(\text{GF} (q^{m'})\), \(m'\leq m ...
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Quantum MDS codes from BCH constacyclic codes
Quantum Information Processing, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liqin Hu, Qin Yue, Xianmang He
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2017
In this chapter, we study polycyclic, negacyclic, constacyclic, quasicyclic and skew cyclic codes which are all generalizations of the important family of cyclic codes. We describe their algebraic setting and show how to use this setting to classify these families of codes.
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In this chapter, we study polycyclic, negacyclic, constacyclic, quasicyclic and skew cyclic codes which are all generalizations of the important family of cyclic codes. We describe their algebraic setting and show how to use this setting to classify these families of codes.
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Equivalence of constacyclic codes with shift constants of different orders
Designs, Codes and CryptographyLet a and b be two non-zero elements of a finite field Fq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
Reza Dastbasteh +4 more
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Cyclic concatenated codes with constacyclic outer codes
IEEE Transactions on Information Theory, 1992Summary: The known construction of cyclic concatenated codes is based on the fact that the inner code is a cyclic minimal code, the outer code is cyclic, and the lengths of the inner and outer codes are relatively prime. Here, it is shown that if the outer code is a suitably chosen constacyclic code the overall concatenated code is always cyclic ...
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Quantum Cyclic and Constacyclic Codes
IEEE Transactions on Information Theory, 2004Based on classical quaternary constacyclic linear codes, we construct a set of quantum codes with parameters [[(4/sup m/ -1)/3, (4/sup m/ -1)/3 -2(3l + b)m, 4l + b + 2]] where m/spl ges/4, 1/spl les/b/spl les/3, and 12l + 3b < 2 /spl times/ 4/sup /spl lfloor/(m+2)/3/spl rfloor//-1, which are better than the codes in Bierbrauer and Edel (2000).
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