期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 64, 期 4, 页码 2444-2459出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2017.2755682
关键词
Asymmetric quantum code; CSS construction; Feng-Rao bound; nested codes; ramp secret sharing; relative generalized Hamming weight; relative minimum distance; wiretap channel of type II
资金
- Danish Council for Independent Research [DFF-4002-00367]
- Spanish MINECO/FEDER [MTM2015-65764-C2-2-P, MTM2015-69138-REDT]
- University Jaume I [P1-1B2015-02]
Two new constructions of linear code pairs C-2 subset of C-1 are given for which the codimension and the relative minimum distances M-1(C-1, C-2) and M-1(C-2(perpendicular to), C-1(perpendicular to)) are good. By this, we mean that for any two out of the three parameters the third parameter of the constructed code pair is large. Such pairs of nested codes are indispensable for the determination of good linear ramp secret sharing schemes. They can also be used to ensure reliable communication over asymmetric quantum channels. The new constructions result from carefully applying the Feng-Rao bounds to a family of codes defined from multivariate polynomials and Cartesian product point sets.
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