Related papers: Constructing Optimal Authentication Codes with Per…
In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…
In this paper we analyse the construction of identification codes. Identification codes are based on the question "Is the message I have just received the one I am interested in?", as opposed to Shannon's transmission, where the receiver is…
We introduce I/O-optimal certifying algorithms for bipartite graphs, as well as for the classes of split, threshold, bipartite chain, and trivially perfect graphs. When the input graph is a class member, the certifying algorithm returns a…
Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the…
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…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Duplicate detection is the problem of identifying whether a given item has previously appeared in a (possibly infinite) stream of data, when only a limited amount of memory is available. Unfortunately the infinite stream setting is…
In this paper, we present two new constructions of complex codebooks with multiplicative characters, additive characters and trace functions over finite fields, and determine the maximal cross-correlation amplitude of these codebooks. We…
This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…
Sphinx, a hardware-software co-design architecture for binary code and runtime obfuscation. The Sphinx architecture uses binary code diversification and self-reconfigurable processing elements to maintain application functionality while…
We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…
In the present paper we introduce and study finite point subsets of a special kind, called optimum distributions, in the n-dimensional unit cube. Such distributions are closely related with known (delta,s,n)-nets of low discrepancy. It…
The intersection problem for additive (extended and non-extended) perfect codes, i.e. which are the possibilities for the number of codewords in the intersection of two additive codes C1 and C2 of the same length, is investigated. Lower and…
Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical…
We investigate optimal encoding and retrieval of digital data, when the storage/communication medium is described by quantum mechanics. We assume an m-ary alphabet with arbitrary prior distribution, and an n-dimensional quantum system.…
Approximation of the optimal two-part MDL code for given data, through successive monotonically length-decreasing two-part MDL codes, has the following properties: (i) computation of each step may take arbitrarily long; (ii) we may not know…
Constructing Reed-Solomon (RS) codes that can correct insertion and deletion (ins-del) errors has been the focus of several recent studies. However, efficient decoding algorithms for such codes have received less attention and remain a…
In Index coding there is a single sender with multiple messages and multiple receivers each wanting a different set of messages and knowing a different set of messages a priori. The Index Coding problem is to identify the minimum number of…
We provide an algorithm to construct unitary matrices over finite fields. We present various constructions of Hermitian self-dual code by means of unitary matrices, where some of them generalize the quadratic double circulant constructions.…
Spatially-coupled (SC) codes are a family of graph-based codes that have attracted significant attention thanks to their capacity approaching performance and low decoding latency. An SC code is constructed by partitioning an underlying…