TY - GEN
T1 - On Levenshtein Balls with Radius One
AU - Bar-Lev, Daniella
AU - Etzion, Tuvi
AU - Yaakobi, Eitan
N1 - Publisher Copyright: © 2021 IEEE.
PY - 2021/7/12
Y1 - 2021/7/12
N2 - The rapid development of DNA storage has brought the deletion and insertion channel, once again, to the front line of research. When the number of deletions is equal to the number of insertions, the Fixed Length Levenshtein (FLL) metric is the right measure for the distance between two words of the same length. The size of a ball is one of the most fundamental parameters in any metric. The size of the ball with radius one in the FLL metric depends on the number of runs and the length of the alternating segments of the given word. In this work, we find the minimum, maximum, and average size of a ball with radius one, in the FLL metric. The related minimum and maximum sizes of a maximal anticode with diameter one are also calculated.
AB - The rapid development of DNA storage has brought the deletion and insertion channel, once again, to the front line of research. When the number of deletions is equal to the number of insertions, the Fixed Length Levenshtein (FLL) metric is the right measure for the distance between two words of the same length. The size of a ball is one of the most fundamental parameters in any metric. The size of the ball with radius one in the FLL metric depends on the number of runs and the length of the alternating segments of the given word. In this work, we find the minimum, maximum, and average size of a ball with radius one, in the FLL metric. The related minimum and maximum sizes of a maximal anticode with diameter one are also calculated.
UR - http://www.scopus.com/inward/record.url?scp=85115084103&partnerID=8YFLogxK
U2 - 10.1109/ISIT45174.2021.9517922
DO - 10.1109/ISIT45174.2021.9517922
M3 - منشور من مؤتمر
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1979
EP - 1984
BT - 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
T2 - 2021 IEEE International Symposium on Information Theory, ISIT 2021
Y2 - 12 July 2021 through 20 July 2021
ER -