Ranks of propelinear perfect binary codes
George K. Guskov, Ivan Yu. Mogilnykh, Faina I. Solov'eva
TL;DR
This paper proves the existence of propelinear perfect binary codes with specific lengths and ranks, expanding the known constructions for these codes in coding theory.
Contribution
It establishes the existence of propelinear perfect binary codes for a wide range of lengths and ranks, except for some specific cases.
Findings
Existence of propelinear perfect binary codes for n=2^m-1, m>=4
Codes cover a broad range of ranks for given lengths
Certain lengths and ranks remain exceptions
Abstract
It is proven that for any numbers n=2^m-1, m >= 4 and r, such that n - log(n+1)<= r <= n excluding n = r = 63, n = 127, r in {126,127} and n = r = 2047 there exists a propelinear perfect binary code of length n and rank r.
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
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research