TRIPLE CIRCULANT CODES BASED ON QUADRATIC RESIDUES

Abstract

One of the most interesting classes of algebraic codes is the class of quadratic residue (QR) codes over a finite field. A natural construction doubling the lengths of QR codes seems to be the double circulant constructions based on quadratic residues given by Karlin, Pless, Gaborit, et. al. In this paper we define a class of triple circulant linear codes based on quadratic residues. We construct many new optimal codes or codes with the highest known parameters using this construction. In particular, we find the first example of a ternary [58, 20, 20] code, which improves the previously known highest minimum distance of any ternary [58, 20] codes.

This article was migrated from the previous system via automation. The abstract may not be written correctly. Please view the PDF file.