In this paper we will estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We will find the length of these codes and we will give a formula for the dimension in terms of the Hilbert function associated to two ideals, one of them being the vanishing ideal of the projective torus. Also we will find an upper bound for the minimum distance and, i...

From ds-bounds for cyclic codes to true distance for abelian codes. Abstract In this paper we develop a technique to extend any bound for the minimum distance of cyclic codes constructed from its defining sets (ds-bounds) to abelian (or multivariate) codes through the notion of B-apparent distance. We use this technique to improve the searching for new bounds for the minimum distance of abelian...

In this paper, we study embedding efficiency, which is an important attribute of steganographic schemes directly influencing their security. It is defined as the expected number of embedded random message bits per one embedding change. Constraining ourselves to embedding realized using linear covering codes (so called matrix embedding), we show that the quantity that determines embedding effici...

ABSTRACT: Space time block code is a transmit diversity strategy used in MIMO technology. STBC-OD design is an attractive code which is having the property of full code rate and full diversity and single symbol decoding for two transmit antennas. Whereas this codes fails for the rate-1 transmission of more than two transmit antennas with the complex signal constellations. To achieve a full code...

One of the main weakness of the family of centralizer codes is that its length is always n. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form nk. We establish two decoding methods which can be fitted to intertwining codes as well as for any linear codes. We also show an inclusion of linear codes into a specia...

Let p be a prime number. In this paper, we study cyclic codes over the ring Z p [u, v]/u 2 , v 2 , uv − vu. We find a unique set of generators for these codes. We also study the rank and the Hamming distance of these codes. We obtain all except one ternary optimal code of length 12 as the Gray image of the cyclic codes over the ring Z p [u, v]/u 2 , v 2 , uv − vu. We also characterize the p-ary...

We develop two new designs of unitary differential space-time modulation (DSTM) with low decoding complexity. Their decoder can be separated into a few parallel decoders, each of which has a decoding search space of less than N if the DSTM codebook contains N codewords. Both designs are based on the concept of joint modulation, which means that several information symbols are jointly modulated,...

The product code proposed in this chapter is constructed by using time-invariant convolutional code. Its component codes’ trellis structure does not vary in time as in product codes constructed with Hamming, BCH, and Reed Solomon block codes. Moreover, the number of states in the trellis structure of a block code may grow exponentially with the difference of codeword and data block lengths, whe...

This paper is concerned with the trellis structure of linear block codes. The paper consists of four parts. In the first part, we investigate the state and branch complexities of a trellis diagram for a linear block code. A trellis diagram with the minimum number of states is said to be minimal. First, we express the branch complexity of a minimal trellis diagram for a linear block code in term...

In this paper, a block code technique is proposed to increase the data rate and to reduce the symbol error rate for the wireless communication. The designed space time block code (STBC) is compared with golden code 2x2, silver code 2x2. STBC is used to realize the diversity gain and provide the remarkable performance in wireless communication systems using MIMO. STBC is based on improved Quasi ...