Generalizing even-like duadic cyclic codes and Type-II duadic negacyclic codes, we introduce even-like (i.e.,Type-II) and odd-like duadic constacyclic codes, and study their properties and existence. We show that even-like duadic constacyclic codes are isometrically orthogonal, and the duals of even-like duadic constacyclic codes are odd-like duadic constacyclic codes. We exhibit necessary and ...

We consider the algorithmic problem of computing a primitive idempotent central simple algebra over field rational functions finite field. The is given by set structure constants. reduced to computation division Brauer equivalent algebra. This constructed as cyclic algebra, once Hasse invariants have been computed. give an application skew constacyclic convolutional codes.

(1+pw)-constacyclic codes of arbitrary length over the nonprincipal ideal ring Zps + uZps are studied, where p is a prime, w ∈ Z × ps and s an integer satisfying s ≥ 2. First, the structure of any (1 + pw)constacyclic code over Zps +uZps are presented. Then enumerations for the number of all codes and the number of codewords in each code, and the structure of dual codes for these codes are give...

One of the main challenges of coding theory is to construct linear codes with the best possible parameters. Various algebraic and combinatorial methods along with computer searches are used to construct codes with better parameters. Given the computational complexity of determining the minimum distance of a code, exhaustive searches are not feasible for all but small parameter sets. Therefore, ...

For units δ and α in Fpm, the structure of (δ + αu 2)-constacyclic codes of length p over Fpm + uFpm + u 2 Fpm is studied and self-dual (δ + αu 2)constacyclic codes are analyzed.

Let $R=\mathbb{Z}_4+u\mathbb{Z}_4,$ where $\mathbb{Z}_4$ denotes the ring of integers modulo $4$ and $u^2=0$. In the present paper, we introduce a new Gray map from $R^n$ to $\mathbb{Z}_{4}^{2n}.$ We study $(1+2u)$-constacyclic codes over $R$ of odd lengths with the help of cyclic codes over $R$. It is proved that the Gray image of $(1+2u)$-constacyclic codes of length $n$ over $R$ are cyclic c...

In this paper, we study the complementary dual codes in more general setting (which are called Galois LCD codes) by a uniform method. A necessary and sufficient condition for linear codes to be Galois LCD codes is determined, and constacyclic codes to be Galois LCD codes are characterized. Some illustrative examples which constacyclic codes are Galois LCD MDS codes are provided as well. In part...

Let p be an odd prime, s,m be positive integers and Fpm be the finite field with p m elements. In this paper, we determine all constacyclic codes of length 4p over the finite commutative chain ring R = Fpm + uFpm with unity, where u 2 = 0. We also determine their dual codes and list some isodual constacyclic codes of length 4p over R.

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...