We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result—which applies to degenerate as well as nondegenerate codes— previously established necessary conditions for classical linear codes can be easily translated into ne...

Generalized pair weights of linear codes are generalizations minimum symbol-pair weights, which were introduced by Liu and Pan (2022) recently. can be used to characterize the ability protecting information in read wire-tap channels type II. In this paper, we introduce notion generalized <...

In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes  enjoy nice algebraic properties just as the classic one.

Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual [n, k] codes with the largest minimum weight among all binary linear complementary dual [n, k] codes. We characterize binary linear complementary dual codes with the largest minimum weight for small dimensions. A complete ...

We obtain a characterization on self-orthogonality for given binary linear code in terms of the number column vectors its generator matrix, which extends result Bouyukliev et al. (2006). As an application, we give algorithmic method to embed k-dimensional C ( k = 3,4) into self-orthogonal shortest l...