TY - GEN
T1 - Bounds on Box Codes
AU - Langberg, Michael
AU - Schwartz, Moshe
AU - Tamo, Itzhak
N1 - Publisher Copyright:
© 2025 IEEE.
PY - 2025
Y1 - 2025
N2 - Let nq(M, d) be the minimum length of a q-ary code of size M and minimum distance d. Bounding nq(M, d) is a fundamental problem that lies at the heart of coding theory. This work considers a generalization nq•(M, d) of nq(M, d) corresponding to codes in which codewords have protected and unprotected entries; where (analogs of) distance and of length are measured with respect to protected entries only. Such codes, here referred to as box codes, have seen prior studies in the context of bipartite graph covering. Upper and lower bounds on nq• •(M, d) are presented.
AB - Let nq(M, d) be the minimum length of a q-ary code of size M and minimum distance d. Bounding nq(M, d) is a fundamental problem that lies at the heart of coding theory. This work considers a generalization nq•(M, d) of nq(M, d) corresponding to codes in which codewords have protected and unprotected entries; where (analogs of) distance and of length are measured with respect to protected entries only. Such codes, here referred to as box codes, have seen prior studies in the context of bipartite graph covering. Upper and lower bounds on nq• •(M, d) are presented.
UR - https://www.scopus.com/pages/publications/105022007903
U2 - 10.1109/ISIT63088.2025.11195455
DO - 10.1109/ISIT63088.2025.11195455
M3 - Conference contribution
AN - SCOPUS:105022007903
T3 - IEEE International Symposium on Information Theory - Proceedings
BT - ISIT 2025 - 2025 IEEE International Symposium on Information Theory, Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2025 IEEE International Symposium on Information Theory, ISIT 2025
Y2 - 22 June 2025 through 27 June 2025
ER -