
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.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · SARS-CoV-2 detection and testing
