Bounds on Box Codes
Michael Langberg, Moshe Schwartz, Itzhak Tamo

TL;DR
This paper introduces bounds on a generalized version of code length for box codes, which are codes with protected and unprotected entries, extending classical bounds in coding theory.
Contribution
It provides the first bounds on the length of box codes, a generalization involving protected entries, expanding understanding of code structures with partial protection.
Findings
Derived upper bounds on box code lengths
Established lower bounds for box code parameters
Extended classical coding bounds to the box code setting
Abstract
Let be the minimum length of a -ary code of size and minimum distance . Bounding is a fundamental problem that lies at the heart of coding theory. This work considers a generalization of corresponding to codes in which codewords have \emph{protected} and \emph{unprotected} entries; where (analogs of) distance and of length are measured with respect to protected entries only. Such codes, here referred to as \emph{box codes}, have seen prior studies in the context of bipartite graph covering. Upper and lower bounds on are presented.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsError Correcting Code Techniques · Cellular Automata and Applications
