Related papers: Construction of Additive Complementary Dual Codes …
In this paper, we investigate the structure and properties of additive complementary dual (ACD) codes over the mixed alphabet $\mathbb{F}_2\mathbb{F}_4$ relative to a certain inner product defined over $\mathbb{F}_2\mathbb{F}_4$. We…
Two families of complementary codes over finite fields $\mathbb{F}_q$ are studied, where $q=r^2$ is square: i) Hermitian complementary dual linear codes, and ii) trace Hermitian complementary dual subfield linear codes. Necessary and…
A linear code is linear complementary dual (LCD) if it meets its dual trivially. LCD codes have been a hot topic recently due to Boolean masking application in the security of embarked electronics (Carlet and Guilley, 2014). Additive codes…
Additive conjucyclic codes over $\F_{q^2}$ are closed under the conjugated cyclic shift and play an important role in constructing quantum error-correcting codes (QECCs). However, a systematic algebraic theory for such codes over general…
The applications of additive codes mainly lie in quantum error correction and quantum computing. Due to their applications in quantum codes, additive codes have grown in importance. In addition to this, additive codes allow the…
We introduce two constructions of additive codes over finite fields. Both constructions start with a linear code over a field with $q$ elements and give additive codes over the field with $q^h$ elements whose minimum distance is…
Codes which have a finite field $\mathbb{F}_{q^m}$ as their alphabet but which are only linear over a subfield $\mathbb{F}_q$ are a topic of much recent interest due to their utility in constructing quantum error correcting codes. In this…
In this paper, we prove existence of optimal complementary dual codes (LCD codes) over large finite fields. We also give methods to generate orthogonal matrices over finite fields and then apply them to construct LCD codes. Construction…
Additive codes have attracted considerable attention for their potential to outperform linear codes. However, distinguishing strictly additive codes from those that are equivalent to linear codes remains a fundamental challenge. To resolve…
This paper investigates the algebraic structure of additive complementary pairs of cyclic codes over a finite commutative ring. We demonstrate that for every additive complementary pair of additive cyclic codes, both constituent codes are…
Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual are trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…
We present a general construction of asymmetric quantum codes based on additive codes under the trace Hermitian inner product. Various families of additive codes over $\F_{4}$ are used in the construction of many asymmetric quantum codes…
Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information…
We investigate additive cyclic codes over the alphabet $\mathbb{F}_{q}\mathbb{F}_{q^2}$, where $q$ is a prime power. First, its generator polynomials and minimal spanning set are determined. Then, examples of $\mathbb{F}_{q^2}$-additive…
Linear codes with complementary duals are linear codes whose intersection with their duals are trivial, shortly named LCD codes. In this paper we outline a construction for LCD codes over finite fields of order $q$ using weighing matrices…
We provide an algorithm to construct unitary matrices over finite fields. We present various constructions of Hermitian self-dual code by means of unitary matrices, where some of them generalize the quadratic double circulant constructions.…
In this paper, we study quasi-twisted codes and their relationship with additive constacyclic codes through a polynomial-based approach. We first present a polynomial characterization of quasi-twisted codes over finite fields analogous to…
The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of…
Linear complementary dual codes (LCD) intersect trivially with their dual. In this paper, we develop a new characterization for LCD codes, which allows us to judge the complementary duality of linear codes from the codeword level. Further,…
An additive code is an $\mathbb{F}_q$-linear subspace of $\mathbb{F}_{q^m}^n$ over $\mathbb{F}_{q^m}$, which is not a linear subspace over $\mathbb{F}_{q^m}$. Linear complementary pairs (LCP) of codes have important roles in cryptography,…