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The construction of quantum error-correcting codes (QECCs) with good parameters is a hot topic in the area of quantum information and quantum computing. Quantum maximum distance separable (QMDS) codes are optimal because the minimum…
A cross-bifix-free code of length $n$ over $\mathbb{Z}_q$ is defined as a non-empty subset of $\mathbb{Z}_q^n$ satisfying that the prefix set of each codeword is disjoint from the suffix set of every codeword. Cross-bifix-free codes have…
Perfect space-time codes were first introduced by Oggier et. al. to be the space-time codes that have full rate, full diversity-gain, non-vanishing determinant for increasing spectral efficiency, uniform average transmitted energy per…
Orthogonal designs are fundamental mathematical notions used in the construction of space time block codes for wireless transmissions. Designs have two important parameters, the rate and the decoding delay; the main problem of the theory is…
Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important role in coding theory. In this paper, we study some results on GQC codes over $\mathbb{Z}_4$ including the normalized generating…
Golomb and Welch conjectured in 1970 that there only exist perfect Lee codes for radius $t=1$ or dimension $n=1, 2$. It is admitted that the existence and the construction of quasi-perfect Lee codes have to be studied since they are the…
We consider codes over the alphabet Q={0,1,..,q-1}intended for the control of unidirectional errors of level l. That is, the transmission channel is such that the received word cannot contain both a component larger than the transmitted one…
Based on ideas of K\"otter and Kschischang we use constant dimension subspaces as codewords in a network. We show a connection to the theory of q-analogues of a combinatorial designs, which has been studied in Braun, Kerber and Laue as a…
The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The…
We characterize group symmetries of poly-phase complementary code matrices (CCMs), which we use to classify CCMs in terms of their equivalence classes. We also present classification results for CCMs of dimension $N\times 4$ where…
This letter proposes a direct construction for cross Z-complementary sets (CZCSs) with flexible lengths and a large zero correlation zone (ZCZ). CZCS is an extension of the cross Z-complementary pair (CZCP). The maximum possible ZCZ width…
Constant dimension codes (CDCs), as special subspace codes, have received extensive attention due to their applications in random network coding. The basic problem of CDCs is to determine the maximal possible size $A_q(n,d,\{k\})$ for given…
This paper introduces a novel class of code sets, called "symmetrical Z-complementary code sets (SZCCSs)" , whose aperiodic auto- and cross- correlation sums exhibit zero-correlation zones (ZCZs) at both the front-end and tail-end of the…
A class of powerful $q$-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are $q$-ary block codes that encode $k$…
A linear code with parameters $[n, k, n - k + 1]$ is called maximum distance separable (MDS), and one with parameters $[n, k, n - k]$ is called almost MDS (AMDS). A code is near-MDS (NMDS) if both it and its dual are AMDS. NMDS codes…
We study LDPC codes for the channel with input ${x}\in \mathbb{F}_q^m$ and output ${y}={x}+{z}\in \mathbb{F}_q^m$. The aim of this paper is to evaluate decoding performance of $q^m$-ary non-binary LDPC codes for large $m$. We give density…
A locally recoverable code of locality $r$ over $\mathbb{F}_{q}$ is a code where every coordinate of a codeword can be recovered using the values of at most $r$ other coordinates of that codeword. Locally recoverable codes are efficient at…
Flag codes generalize constant dimension codes by considering sequences of nested subspaces with prescribed dimensions as codewords. A comprehensive construction, which unites cyclic orbit flag codes, yields two families of flag codes on…
A (q,k,t)-design matrix is an m x n matrix whose pattern of zeros/non-zeros satisfies the following design-like condition: each row has at most q non-zeros, each column has at least k non-zeros and the supports of every two columns…
Linear codes with complementary duals (abbreviated LCD) are linear codes whose intersection with their dual is trivial. When they are binary, they play an important role in armoring implementations against side-channel attacks and fault…