منابع مشابه
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.
متن کاملGalois 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
متن کاملOn 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...
متن کاملA 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...
متن کاملComplementary Dual Subfield Linear Codes Over Finite Fields
Two families of complementary codes over finite fields q are studied, where 2 = q r is square: i) Hermitian complementary dual linear codes, and ii) trace Hermitian complementary dual subfield linear codes. Necessary and sufficient conditions for a linear code (resp., a subfield linear code) to be Hermitian complementary dual (resp., trace Hermitian complementary dual) are determined. Construct...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2019
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2019.2907276