Related papers: Old and New Results on Alphabetic Codes
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
Random access codes are a type of communication task that is widely used in quantum information science. The optimal average success probability that can be achieved through classical strategies is known for any random access code. However,…
Algorithms which compute properties over graphs have always been of interest in computer science, with some of the fundamental algorithms, such as Dijkstra's algorithm, dating back to the 50s. Since the 70s there as been interest in…
After the pursuit of seventy years, the invention of polar codes indicates that we have found the first capacity-achieving coding with low complexity construction and decoding, which is the great breakthrough of the coding theory in the…
Separating codes have their applications in collusion-secure fingerprinting for generic digital data, while they are also related to the other structures including hash family, intersection code and group testing. In this paper we study…
This paper attempts to connects the evolution of computer languages with the evolution of life, where the later has been dictated by \emph{theory of evolution of species}, and tries to give supportive evidence that the new languages are…
A lot of attention has been paid to the investigation of the algebraic properties of linear codes. In most cases, this investigation involves the determination of required code automorphisms, which are useful for decoders, such as the…
Bounds on linear codes play a central role in coding theory, as they capture the fundamental trade-off between error-correction capability (minimum distance) and information rate (dimension relative to length). Classical results…
In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications, the data to be transmitted may lie (or can be well approximated) in a…
In this paper we describe a variation of the classical permutation decoding algorithm that can be applied to any affine-invariant code with respect to certain type of information sets. In particular, we can apply it to the family of…
New families of unit memory as well as multi-memory convolutional codes are constructed algebraically in this paper. These convolutional codes are derived from the class of group character codes. The proposed codes have basic generator…
Cyclic codes have many applications in consumer electronics, communication and data storage systems due to their efficient encoding and decoding algorithms. An efficient approach to constructing cyclic codes is the sequence approach. In…
The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of…
Decoding of convolutional codes poses a significant challenge for coding theory. Classical methods, based on e.g. Viterbi decoding, suffer from being computationally expensive and are restricted therefore to codes of small complexity. Based…
Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum…
Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning techniques to impressive results in regression, classification, data-generation and reinforcement learning tasks.…
Background: Transitioning from an old medical coding system to a new one can be challenging, especially when the two coding systems are significantly different. The US experienced such a transition in 2015. Objective: This research aims to…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
A novel code construction algorithm is presented to find all the possible code families for code reconfiguration in an OCDMA system. The algorithm is developed through searching all the complete subgraphs of a constructed graph. The…
Code super-optimization is the task of transforming any given program to a more efficient version while preserving its input-output behaviour. In some sense, it is similar to the paraphrase problem from natural language processing where the…