In this paper we introduce self-dual cyclic and quantum codes over Zα2 × (Z2 + uZ2) . We determine the conditions for any Z2Z2[u]-cyclic code to be self-dual, that is, C = C. Since the binary image of a selforthogonal Z2Z2[u]-linear code is also a self-orthogonal binary linear code, we introduce quantum codes over Zα2 × (Z2 + uZ2) β . Finally, we present some examples of self-dual cyclic and qu...

In [8], the codewords of small weight in the dual code of the code of points and lines of Q(4, q) are characterized. Using geometrical arguments, we characterize the codewords of small weight in the dual code of the code of points and generators of Q(5, q) and H(5, q). For the dual codes of the codes of Q(5, q), q even, and Q(4, q), q even, we investigate the codewords with the largest weights....

It is shown that the residue code of a self-dual Z4-code of length 24k (resp. 24k + 8) and minimum Lee weight 8k + 4 or 8k + 2 (resp. 8k + 8 or 8k + 6) is a binary extremal doubly even self-dual code for every positive integer k. A number of new self-dual Z4-codes of length 24 and minimum Lee weight 10 are constructed using the above characterization.

In this paper we study n ∏ i=1 Z2i -Additive Cyclic Codes. These codes are identified as Z2n [x]submodules of n ∏ i=1 Z2i [x]/〈x αi − 1〉; αi and i being relatively prime for each i = 1, 2, . . . , n. We first define a n ∏ i=1 Z2i -additive cyclic code of a certain length. We then define the distance between two codewords and the minimum distance of such a code. Moreover we relate these to binar...

in this research, shielding and criticality safety calculations carried out for interim storage and transportation cask in the tehran research reactor. such dual purpose cask is being designed to the spent fuel elements of research reactors. the monte carlo mcnp5 code calculation was utilized for the criticality safety analysis and origen2.1code was used for shielding calculation. according to ...

An important class of codes widely used in applications is the class of convolutional codes. Most of the literature of convolutional codes is devoted to convolutional codes over finite fields. The extension of the concept of convolutional codes from finite fields to finite rings have attracted much attention in recent years due to fact that they are the most appropriate codes for phase modulati...

Let H be a Hadamard matrix of order 24. In this note, we show that the extremality of the binary code of H is equivalent to the extremality of the ternary code of HT . This fact has been observed by Assmus and Key [1], as a result of the complete classification of Hadamard matrices of order 24. Our proof is a consequence of more general results on the minimum weight of the dual code of the code...

Abstmt. It is showc that for any block length n which is a multiple of 5, there exists a binary self dual code irr which all weights are divisible by 4, and the minimum weight is asymptotically the same as that given by the Varshamov-Gilbert bound. § 1. Preliminaries Let Fn denote the vector space of all vectors of length II with components from GF(2). The weiglzt of ii vector u = is the number...

Tietäväinen’s upper and lower bounds assert that for block-length-n linear codes with dual distance d, the covering radius R is at most n2 − ( 2 − o(1)) √ dn and typically at least n2 − Θ( √ dn log nd ). The gap between those bounds on R − n2 is an Θ( √ log nd ) factor related to the gap between the worst covering radius given d and the sphere-covering bound. Our focus in this paper is on the c...