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Three new constructions of optimal linear codes with few weights
Linear codes play a key role in widespread applications. In this paper, we propose three new constructions of linear codes. We give some sufficient...
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A Hadamard Product of Linear Codes: Algebraic Properties and Algorithms for Calculating It
AbstractA study is performed of the algebraic properties of the Hadamard product (Schur product, component-wise product) of linear error-correcting...
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On symplectic hulls of linear codes and related applications
This paper investigates symplectic hulls of linear codes. We use a different view to obtain more structural properties of generator matrices with...
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A Go-Up Code Construction from Linear Codes Yielding Additive Codes for Quantum Stabilizer Codes
Given a code C over the finite field \(\mathbb {F}_q\) ,...
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Linear complementary pairs of codes over a finite non-commutative Frobenius ring
In this paper, we study linear complementary pairs (LCP) of codes over finite non-commutative local rings. We further provide a necessary and...
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The maximum number of homogeneous weights of linear codes over chain rings
The problem of determining the largest possible number of distinct Hamming weights in several classes of codes over finite fields was studied...
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One more proof of the first linear programming bound for binary codes and two conjectures
We give one more proof of the first linear programming bound for binary codes, following the line of work initiated by Friedman and Tillich [9]. The...
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Binary optimal linear codes with various hull dimensions and entanglement-assisted QECCs
The hull of a linear code C is the intersection of C with its dual. To the best of our knowledge, there are very few constructions of binary linear...
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New MRD codes from linear cutting blocking sets
Minimal rank-metric codes or, equivalently, linear cutting blocking sets are characterized in terms of the second generalized rank weight, via their...
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Error-correcting codes based on partial linear maps of finite-dimensional vector spaces
The determination of bounds on the size of codes with given minimum distance is an important problem in the coding theory. In this paper, we...
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Infinite families of optimal linear codes and their applications to distributed storage systems
Linear codes with large minimum distances perform well in error and erasure corrections. Constructing such linear codes is a main topic in coding...
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Quantum synchronizable codes from repeated-root quasi-cyclic codes
Quantum synchronizable codes are generally constructed from cyclic codes. In this paper, we extend the class of codes available for constructing...
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Three-weight linear codes from Weil sums
By appropriately choosing a defining set, we define a class of linear codes and establish their complete weight enumerators and weight enumerators...
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Entanglement-assisted quantum error-correcting codes from subfield subcodes of projective Reed–Solomon codes
We study the subfield subcodes of projective Reed–Solomon codes and their duals: we provide bases for these codes and estimate their parameters. With...
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A novel coding scheme for generating sixteen codes from quaternary codes with applications
Digital data transmission and storage are indispensable components for our contemporary information-driven society. As data volumes keep increasing,...
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Matrix product and quasi-twisted codes in one class
Many classical constructions, such as Plotkin’s and Turyn’s, were generalized by matrix product (MP) codes. Quasi-twisted (QT) codes, on the other...
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Constructions of Codes with Weighted Poset Block Metrics
Weighted poset block metric is a generalization of two types of metrics: one is weighted poset metric introduced by Panek and Pinheiro (
2010 ) and the...