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THE TWICE-EXTENDED TGRS CODES
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DOI：10.3934/amc.2026027.png)
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Abstract
En 中文
Maximum distance separable (MDS) codes and near MDS (NMDS) codes play a fundamental role in coding theory due to their maximal errorcorrecting capabilities and rich algebraic structure. This paper constructs a new class of linear codes by twice extending TGRS codes, denoted as Ck,n,lambda 1,lambda 2,delta(alpha, v, oo). First, we establish the necessary and sufficient conditions for Ck,n,lambda 1,lambda 2,delta (alpha, v, oo) to be MDS. By analyzing the AMDS properties of both Ck,n,lambda 1,lambda 2,delta(alpha, v, oo) and their duals Ck,n,lambda 1,lambda 2,delta(alpha, v, oo)perpendicular to, we determine the necessary and sufficient conditions for Ck,n,lambda 1,lambda 2,delta(alpha, v, oo) to be NMDS. Besides, we provide the form of the parity check matrix for Ck,n,lambda 1,lambda 2,delta(alpha, v, oo) and characterize the weight distributions of both the codes Ck,n,lambda 1,lambda 2,delta (alpha, v, oo) and their duals. Additionally, using the Schur method, the non-generalized Reed-Solomon (non-GRS) properties are proven. Finally, several classes of linear complementary dual (LCD) codes are constructed.
Keywords:
MDS code
NMDS code
LCD code
non-GRS
TGRS code
Journal
A
IF:
0.7
Papers:
59
Citations:
0