Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors

Hengjia Wei; Moshe Schwartz

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arXiv · 2201.01558

Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors

Hengjia Wei·Moshe Schwartz

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Abstract

Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error ball. We construct two classes of such perfect codes correcting a single burst of length $2$ for $(1,0)$-limited-magnitude errors, both for cyclic and non-cyclic bursts. We also present a generic construction that requires a primitive element in a finite field with specific properties. We then show that in various parameter regimes such primitive elements exist, and hence, infinitely many perfect burst-correcting codes exist.

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Hengjia Wei, Moshe Schwartz. 2022-01-05. Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors. https://arxiv.org/abs/2201.01558

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