573 research outputs found
New MDS self-dual codes over finite fields \F_{r^2}
MDS self-dual codes have nice algebraic structures and are uniquely
determined by lengths. Recently, the construction of MDS self-dual codes of new
lengths has become an important and hot issue in coding theory. In this paper,
we develop the existing theory and construct six new classes of MDS self-dual
codes. Together with our constructions, the proportion of all known MDS
self-dual codes relative to possible MDS self-dual codes generally exceed 57\%.
As far as we know, this is the largest known ratio. Moreover, some new families
of MDS self-orthogonal codes and MDS almost self-dual codes are also
constructed.Comment: 16 pages, 3 tabl
Research on Hermitian self-dual codes, GRS codes and EGRS codes
MDS self-dual codes have nice algebraic structures, theoretical significance
and practical implications. In this paper, we present three classes of
-ary Hermitian self-dual (extended) generalized Reed-Solomon codes with
different code locators. Combining the results in Ball et al. (Designs, Codes
and Cryptography, 89: 811-821, 2021), we show that if the code locators do not
contain zero, -ary Hermitian self-dual (extended) GRS codes of length
does not exist. Under certain conditions, we prove Conjecture
3.7 and Conjecture 3.13 proposed by Guo and Li et al. (IEEE Communications
Letters, 25(4): 1062-1065, 2021).Comment: 18 page
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