TY - JOUR
T1 - Hierarchical erasure correction of linear codes
AU - Raviv, Netanel
AU - Schwartz, Moshe
AU - Cohen, Rami
AU - Cassuto, Yuval
N1 - Funding Information:
Moshe Schwartz was supported in part by a German Israeli Project Cooperation (DIP) grant under grant no. PE2398/1-1. Yuval Cassuto was supported in part by the US-Israel Binational Science Foundation under grant no. 2016703 and in part by the Israeli Science Foundation under grant no. 2525/19.
Funding Information:
Moshe Schwartz was supported in part by a German Israeli Project Cooperation (DIP) grant under grant no. PE2398/1-1 . Yuval Cassuto was supported in part by the US-Israel Binational Science Foundation under grant no. 2016703 and in part by the Israeli Science Foundation under grant no. 2525/19 .
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - Linear codes over finite extension fields have widespread applications in theory and practice. In some scenarios, the decoder has a sequential access to the codeword symbols, giving rise to a hierarchical erasure structure. In this paper we develop a mathematical framework for hierarchical erasures over extension fields, provide several bounds and constructions, and discuss potential applications in distributed storage and flash memories. Our results show intimate connection to Universally Decodable Matrices, as well as to Reed-Solomon and Gabidulin codes.
AB - Linear codes over finite extension fields have widespread applications in theory and practice. In some scenarios, the decoder has a sequential access to the codeword symbols, giving rise to a hierarchical erasure structure. In this paper we develop a mathematical framework for hierarchical erasures over extension fields, provide several bounds and constructions, and discuss potential applications in distributed storage and flash memories. Our results show intimate connection to Universally Decodable Matrices, as well as to Reed-Solomon and Gabidulin codes.
KW - Erasure-correcting codes
KW - Hierarchical erasures
KW - Linear codes
UR - http://www.scopus.com/inward/record.url?scp=85090139589&partnerID=8YFLogxK
U2 - 10.1016/j.ffa.2020.101743
DO - 10.1016/j.ffa.2020.101743
M3 - Article
AN - SCOPUS:85090139589
SN - 1071-5797
VL - 68
JO - Finite Fields and Their Applications
JF - Finite Fields and Their Applications
M1 - 101743
ER -