May 18 – 22, 2026
Virginia Tech
America/New_York timezone

Code Rigidity in Characteristic 2

May 21, 2026, 11:25 AM
25m
Goodwin Hall 125 (Virginia Tech)

Goodwin Hall 125

Virginia Tech

Minisymposium Talk Code-based Cryptography Code-based Cryptography

Speaker

Adam Downs (Virginia Tech)

Description

Two linear codes are equivalent if there exists a monomial matrix that transforms one to the other. The problem of finding a monomial transformation from one code to another underlies the Linear Equivalence Signature Scheme (LESS). An automorphism of a linear code is a monomial matrix which fixes the code. When a code has a large number of automorphisms, it is easier to solve the linear code equivalence problem; thus, it is desirable for cryptography to have codes with as few automorphisms as possible. A code with the smallest possible number of automorphisms is called rigid.

Prior results show that almost all binary codes of dimension k and length 2k are rigid as k goes to infinity. We extend this result to arbitrary finite fields of characteristic 2.

Author

Adam Downs (Virginia Tech)

Presentation materials

There are no materials yet.