Error-detecting solid codes

TL;DR

This paper extends the construction of variable-length solid codes from binary to n-ary codes and demonstrates an error-detection property with practical applications.

Contribution

It generalizes existing binary code constructions to arbitrary n-ary codes and proves a new error-detection property for a specific subfamily.

Findings

Extension of variable-length solid codes to n-ary alphabets

Proof of an error-detection property for a subfamily of these codes

Application to a specific type of binary code

Abstract

A code is called solid if, roughly speaking, any correctly-transmitted codeword in an arbitrarily corrupted string of codewords can still be decoded correctly and unambiguously. So-called variable-length solid codes, in which codewords may differ in length, have been studied by various authors. In this short note, we observe that a recent construction of variable-length solid codes based on binary codes may be extended to arbitrary n-ary codes. We further prove an interesting error-detection property of a specific subfamily of these variable-length solid codes, and give a concrete application to a certain type of binary code.