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LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality larger than 3. Hence, the study of LCD codes is mainly open for binary and ternary fields. Subfield subcodes of $J$ -affine variety codes are a generalization of BCH codes which have been successfully used for constructing good quantum codes. We describe binary and ternary LCD codes constructed as subfield subcodes of $J$ -affine variety codes and provide some new and good LCD codes coming from this construction. [ABSTRACT FROM AUTHOR]

Two new constructions of linear code pairs C2 \subset C1 are given for which the codimension and the relative minimum distances M1(C1,C2) and M1(C\vphantom {Rj2}^\perp,C1^\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. 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. [ABSTRACT FROM AUTHOR]

Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes. In this paper, we elaborate on the implication of these parameters and devise a method to estimate their value for general one-point algebraic geometric codes. As it is demonstrated, for Hermitian codes, our bound is often tight. Furthermore, for these codes, the relative generalized Hamming weights are often much larger than the corresponding generalized Hamming weights. [ABSTRACT FROM AUTHOR]

We are proud to present this special issue in honor of Ruud Pellikaan. It presents 11 selected papers out of 27 submitted by the participants as postconference contributions of the workshop entitled "Codes, Cryptology and Curves in honour of Ruud Pellikaan" that took place at Eindhoven University of Technology (TU/e) 7-9 March of 2019. As it is impossible to adequately cover all of the recent advances based on Ruud's works in a single issue, we intend to present a fragment of the timely research topics and noteworthy new developments related to his research. [Extracted from the article]