Linear Codes Associated to Skew-symmetric Determinantal Varieties
Peter Beelen, Prasant Singh
TL;DR
This paper studies linear codes derived from skew-symmetric determinantal varieties, determining their minimum distances in odd characteristic and providing a recursive formula for codeword weights.
Contribution
It introduces a new class of linear codes from skew-symmetric determinantal varieties and derives explicit minimum distances and weight formulas.
Findings
Minimum distances are determined in odd characteristic.
A recursive formula for codeword weights is provided.
The codes are characterized by properties of skew-symmetric matrices.
Abstract
In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these codes is given.
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 · Finite Group Theory Research · graph theory and CDMA systems