Improved constructions of nested code pairs
Abstract
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 FengRao bounds [18,27] to a family of codes defined from multivariate polynomials and Cartesian product point sets.
 Publication:

arXiv eprints
 Pub Date:
 October 2016
 arXiv:
 arXiv:1610.06363
 Bibcode:
 2016arXiv161006363G
 Keywords:

 Computer Science  Information Theory;
 Mathematics  Commutative Algebra;
 11T71;
 14G50;
 94B27;
 94B65
 EPrint:
 36 pages