We consider linear codes in the metric space with the Niederreiter-Rosenbloom-Tsfasman (NRT) metric, calling them linear ordered codes. In the first part of the paper we examine a linear-algebraic perspective of linear ordered codes, focusing on the distribution of “shapes” of codevectors. We define a multivariate Tutte polynomial of the linear code and prove a duality relation for the Tutte po...

In this paper we estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We find the length of these codes and we 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 find an upper bound for the minimum distance and, in some cases, we giv...

Multiple-antenna systems that operate at high rates require simple yet effective space-time transmission schemes to handle the large traffic volume in real time. At rates of tens of bits/sec/Hz, V-BLAST, where every antenna transmits its own independent substream of data, has been shown to have good performance and simple encoding and decoding. Yet V-BLAST suffers from its inability to work wit...

Let F be a finite field with q elements. A k dimensional subspace C of the vector space Fn of all n-tuples over F is called a linear code of length n and dimension k. Algebraically, C is just a k-dimensional vector space over F. However, as a particular subspace of Fn, C inherits some metric properties. Specifically, for every v E Fn, the weight of v, denoted by wt( v), is defined to be the num...

For every n = 2 k ≥ 16 there exist exactly ⌊(k + 1)/2⌋ mutually nonequiv-alent Z 4-linear extended perfect codes with distance 4. All these codes have different ranks. Codes represented in such a manner are called Z 4-linear. In [5] it is shown that the extended Golay code and the extended Hamming (n, 2 n−log 2 n−1 , 4)-codes (of length n and cardinality 2 n−log 2 n−1 , with distance 4) for eve...

A linear error-block code is a natural generalization of the classical error-correcting code and has applications in experimental design, high-dimensional numerical integration and cryptography. This article formulates the concept of a linear error-block code and derives basic results for this kind of code by direct analogy to the classical case. Some problems for further research are raised. ©...

A code C is Z2Z4-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C by deleting the coordinates outside X (respectively, Y ) is a binary linear code (respectively, a quaternary linear code). In this paper, the rank and dimension of the kernel for Z2Z4-linear codes, which are the corresponding binary codes of Z2Z4-additive codes, are ...