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Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors (2201.01558v1)
Published 5 Jan 2022 in cs.IT and math.IT
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.