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16.09.2016 | Ausgabe 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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