Affine Grassmann Codes
Peter Beelen, Sudhir R. Ghorpade, and Tom Hoeholdt
TL;DR
Affine Grassmann codes are a new class of linear codes related to Grassmann and Reed-Muller codes, with explicitly determined parameters and large automorphism groups, offering potential advantages in coding theory.
Contribution
This paper introduces affine Grassmann codes, establishing their parameters, automorphism groups, and minimum weight codewords, expanding the landscape of algebraic coding theory.
Findings
Determined length, dimension, and minimum distance of affine Grassmann codes.
Proved affine Grassmann codes have large automorphism groups.
Counted the number of minimum weight codewords.
Abstract
We consider a new class of linear codes, called affine Grassmann codes. These can be viewed as a variant of generalized Reed-Muller codes and are closely related to Grassmann codes. We determine the length, dimension, and the minimum distance of any affine Grassmann code. Moreover, we show that affine Grassmann codes have a large automorphism group and determine the number of minimum weight codewords.
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.