Galois invariance, trace codes and subfield subcodes

Galois invariance, trace codes and subfield subcodes

Article history: Received 26 February 2009 Revised 21 September 2009 Available online 2 February 2010 Communicated by W. Cary Huffman

On parameters of subfield subcodes of extended norm-trace codes

In this article we describe how to find the parameters of subfield subcodes of extended Norm–Trace codes. With a Gröbner basis of the ideal of the Fqr rational points of the Norm–Trace curve one can determine the dimension of the subfield subcodes or the dimension of the trace code. We also find a BCH–like bound from the minimum distance of the original supercode. AMS Subject Classification: Pr...

Quantum codes from affine variety codes and their subfield-subcodes

We use affine variety codes and their subfield-subcodes for obtaining quantum stabilizer codes via the CSS code construction. With this procedure we get codes with good parameters, some of them exceeding the quantum Gilbert-Varshamov bound given by Feng and Ma.

A Linear Algebraic Approach to Subfield Subcodes of GRS Codes

The problem of finding subfield subcodes of generalized Reed–Solomon (GRS) codes (i.e., alternant codes) is considered. A pure linear algebraic approach is taken in order to derive message constraints that generalize the well known conjugacy constraints for cyclic GRS codes and their Bose– Chaudhuri–Hocquenghem (BCH) subfield subcodes. It is shown that the presented technique can be used for fi...

Symmetry Codes and Their Invariant Subcodes