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BCH codes are a special subclass of cyclic codes and have many important applications in data storage and communication systems. In this paper, we investigate the structure of binary linear complementary dual (LCD) BCH codes with length $ n = \frac{{{2^m} + 1}}{3} $, where $ m \geq 7 $ is an odd integer. By exploring cyclotomic cosets modulo $ n $, we determine the dimension of LCD BCH codes for designed distance $ \delta $ in the range $ 2 \le \delta \le{2^{\frac{{m + 1}}{2}}} $. Furthermore, we compute the first five largest coset leaders modulo $ n $ and construct some binary LCD BCH codes. We also present two families of optimal binary linear codes from LCD BCH codes. [ABSTRACT FROM AUTHOR]

Linear codes with complementary dual (LCD codes) play an important role in armoring implementations against side-channel attacks and fault injection attacks. Hermitian LCD codes are a special class of LCD codes, which were proved to be asymptotically good. In this paper, several classes of optimal quaternary Hermitian LCD codes are constructed via constacyclic codes. The binary images of these classes of quaternary Hermitian LCD codes are characterized. Several classes of optimal binary LCD codes with minimum distance 6, and optimal binary linear codes with one-dimensional hull and minimum distance 6 are also presented. [ABSTRACT FROM AUTHOR]

Let Fq be a finite field with character p and p ≠ 3, l ≠ 3 be different odd primes. In this paper, we study constacyclic codes of length 6lps over finite field Fq. The generator polynomials of all constacyclic codes and their duals are obtained. Moreover, we give the characterization and enumeration of linear complementary dual (LCD) and self-dual constacyclic codes of length 6lps over Fq. [ABSTRACT FROM AUTHOR]

In this paper, we construct several classes of maximum distance separable (MDS) codes via generalized Reed-Solomon (GRS) codes and extended GRS codes, where we can determine the dimensions of their Euclidean hulls or Hermitian hulls. It turns out that the dimensions of Euclidean hulls or Hermitian hulls of the codes in our constructions can take all or almost all possible values. As a consequence, we can apply our results to entanglement-assisted quantum error-correcting codes (EAQECCs) and obtain several new families of MDS EAQECCs with flexible parameters. The required number of maximally entangled states of these MDS EAQECCs can take all or almost all possible values. Moreover, several new classes of q-ary MDS EAQECCs of length $ {n} > {q}+1$ are also obtained. [ABSTRACT FROM AUTHOR]

Maximum-distance-separable (MDS) codes and self-dual codes are important families of classical codes in coding theory. It is of interest to investigate MDS self-dual codes. The existence of MDS self-dual codes over finite field F q has been completely solved for q is even. In this paper, for finite field with odd characteristic, we obtain some new results on the existence of MDS self-dual codes by generalized Reed-Solomon (GRS) codes and extended GRS codes. [ABSTRACT FROM AUTHOR]

Let $$R=\mathbb {F}_{2^{m}}+u\mathbb {F}_{2^{m}}+\cdots +u^{k}\mathbb {F}_{2^{m}}$$ , where $$\mathbb {F}_{2^{m}}$$ is the finite field with $$2^{m}$$ elements, m is a positive integer, and u is an indeterminate with $$u^{k+1}=0.$$ In this paper, we propose the constructions of two new families of quantum codes obtained from dual-containing cyclic codes of odd length over R. A new Gray map over R is defined, and a sufficient and necessary condition for the existence of dual-containing cyclic codes over R is given. A new family of $$2^{m}$$ -ary quantum codes is obtained via the Gray map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over R. In particular, a new family of binary quantum codes is obtained via the Gray map, the trace map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over R. [ABSTRACT FROM AUTHOR]