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16.09.2016 | Ausgabe 1-2/2017

Designs, Codes and Cryptography 1-2/2017

Symmetric disjunctive list-decoding codes

Zeitschrift:
Designs, Codes and Cryptography > Ausgabe 1-2/2017
Autoren:
A. G. D’yachkov, I. V. Vorobyev, N. A. Polyanskii, V. Yu. Shchukin
Wichtige Hinweise
The material in this work was presented in part at the 2015 IEEE International Symposium on Information Theory [6]. This paper provides the proofs of all lemmas, which were formulated in [6], (refer to Sect. 2) and contains some improvements of the results, which were developed in [6] (refer to Sects. 1.3, 1.5 and 1.6).
This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.

Abstract

In this work, we consider symmetric disjunctive list-decoding (SLD) codes, which are a class of binary codes based on a symmetric disjunctive sum (SDS) of binary symbols. By definition, the SDS takes values from the ternary alphabet \(\{0, 1, *\}\), where the symbol \(*\) denotes “erasure”. Namely: SDS is equal to 0 (1) if all its binary symbols are equal to 0 (1), otherwise SDS is equal to \(*\). The main purpose of this work is to obtain bounds on the rate of these codes.

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