Error-detecting solid codes

Nathan Thomas Carruth

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arXiv · 2603.20298

Error-detecting solid codes

Nathan Thomas Carruth

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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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Nathan Thomas Carruth. 2026-03-19. Error-detecting solid codes. https://arxiv.org/abs/2603.20298

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