The Subfield Codes of [q+1, 2, q] MDS Codes

08/03/2020
by   Ziling Heng, et al.
0

Recently, subfield codes of geometric codes over large finite fields (q) with dimension 3 and 4 were studied and distance-optimal subfield codes over (p) were obtained, where q=p^m. The key idea for obtaining very good subfield codes over small fields is to choose very good linear codes over an extension field with small dimension. This paper first presents a general construction of [q+1, 2, q] MDS codes over (q), and then studies the subfield codes over (p) of some of the [q+1, 2,q] MDS codes over (q). Two families of dimension-optimal codes over (p) are obtained, and several families of nearly optimal codes over (p) are produced. Several open problems are also proposed in this paper.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset