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Register a new userOn Quantum Stabilizer Codes derived from Local Frobenius Rings
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Added by
Heide Gluesing-Luerssen
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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In this paper we consider stabilizer codes over local Frobenius rings. First, we study the relative minimum distances of a stabilizer code and its reduction onto the residue field. We show that for various scenarios, a free stabilizer code over the ring does not underperform the according stabilizer code over the field. This leads us to conjecture that the same is true for all free stabilizer codes. Secondly, we focus on the isometries of stabilizer codes. We present some preliminary results and introduce some interesting open problems.
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This is a survey on the theory of skew-cyclic codes based on skew-polynomial rings of automorphism type. Skew-polynomial rings have been introduced and discussed by Ore (1933). Evaluation of skew polynomials and sets of (right) roots were first considered by Lam (1986) and studied in great detail by Lam and Leroy thereafter. After a detailed presentation of the most relevant properties of skew polynomials, we survey the algebraic theory of skew-cyclic codes as introduced by Boucher and Ulmer (2007) and studied by many authors thereafter. A crucial role will be played by skew-circulant matrices. Finally, skew-cyclic codes with designed minimum distance are discussed, and we report on two different kinds of skew-BCH codes, which were designed in 2014 and later.
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