arXiv 1610.063632016-10cs.ITmath.ACmath.IT

Improved constructions of nested code pairs

Carlos Galindo, Olav Geil, Fernando Hernando, Diego Ruano

备注：: 36 pages
发表信息：: IEEE Transactions on Information Theory. Volume 64, Issue 4, pages 2444-2459 (2018)
DOI：: 10.1109/TIT.2017.2755682

英文摘要：

Two new constructions of linear code pairs $C_2 \subset C_1$ are given for which the codimension and the relative minimum distances $M_1(C_1,C_2)$, $M_1(C_2^\perp,C_1^\perp)$ 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 [35]. They can also be used to ensure reliable communication over asymmetric quantum channels [47]. The new constructions result from carefully applying the Feng-Rao bounds [18,27] to a family of codes defined from multivariate polynomials and Cartesian product point sets.

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