TY - GEN
T1 - Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors
AU - Wei, Hengjia
AU - Schwartz, Moshe
N1 - Funding Information:
This work was supported in part by the Israel Science Foundation (ISF) under Grant 270/18.
Publisher Copyright:
© 2022 IEEE.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85136255046&partnerID=8YFLogxK
U2 - 10.1109/ISIT50566.2022.9834644
DO - 10.1109/ISIT50566.2022.9834644
M3 - Conference contribution
AN - SCOPUS:85136255046
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1809
EP - 1814
BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022
Y2 - 26 June 2022 through 1 July 2022
ER -