Symmetry Codes and Their Invariant Subcodes
Abstract
The paper defines and studies the invariant subcodes, (R sub sigma) (q) and (R sub mu)(q), of the symmetry code C(q) in order to be able to determine the algebraic properties of these codes. Every vector in (R sub sigma)(q) is invariant under a monomial transformation tau, odd order dividing (q + 1), in the group of C(q). Also (R sub mu)(q) is invariant under tau but not vector-wise. The dimensions of (R sub sigma)(q) and (R sub mu)(q) are determined and relations between these subcodes are given. Also (R sub sigma) (q) is shown to be isomorphic to a self-orthogonal subspace of (V sub 3)((2q + 2)/s). The isomorphic images of (R sub sigma)(17) and (R sub sigma)(29) are both demonstrated to be equivalent to the (12,6) Golay code.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1974
- Accession Number
- AD0780243
Entities
People
- Vera Pless
Organizations
- Massachusetts Institute of Technology