Related papers: New Symbols for Base-16 and Base-256 Numerals

The balanced incomplete block design (BIBD) problem is a difficult combinatorial problem with a large number of symmetries, which add complexity to its resolution. In this paper, we propose a dual (integer) problem representation that…

In this work we propose a new type of shift spaces, called blur shift spaces, where one can represent with a single symbol an entire set of infinite symbols. Such shift spaces are constructed from classical shift spaces, by choosing some…

In this study, we define a new type of Fibonacci and Lucas num- bers which are called bicomplex Fibonacci and bicomplex Lucas numbers. We obtain the well-known properties e.g. Docagnes, Cassini, Catalan for these new types. We also give the…

In this paper will be presented new approach to entropy coding: family of generalizations of standard numeral systems which are optimal for encoding sequence of equiprobable symbols, into asymmetric numeral systems - optimal for freely…

We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized Reed-Solomon codes in the…

Commutative complex numbers of the form u=x+\alpha y+\beta z+\gamma t in 4 dimensions are studied, the variables x, y, z and t being real numbers. Four distinct types of multiplication rules for the complex bases \alpha, \beta and \gamma…

This paper explores the possibilities of using a computing methodology --hardware and software-- that employs technology other than binary. I refer to this as "supra - binary" computing. Software constructs that use more than binary…

This work introduces the Elliptica pseudo-spectral code for generating initial data of binary neutron star systems. Building upon the recent Elliptica code update, we can now construct initial data using not only piecewise polytropic…

This paper is an exploration in a functional programming framework of {\em isomorphisms} between elementary data types (natural numbers, sets, multisets, finite functions, permutations binary decision diagrams, graphs, hypergraphs,…

Whilst there have been great advances in HPC hardware and software in recent years, the languages and models that we use to program these machines have remained much more static. This is not from a lack of effort, but instead by virtue of…

We release Code Llama, a family of large language models for code based on Llama 2 providing state-of-the-art performance among open models, infilling capabilities, support for large input contexts, and zero-shot instruction following…

In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read…

We generalize Helberg's number-theoretic construction of multiple insertion-deletion correcting binary codes to non-binary alphabets and describe a linear decoding algorithm for correcting multiple deletions.

Word embedding is an essential building block for deep learning methods for natural language processing. Although word embedding has been extensively studied over the years, the problem of how to effectively embed numerals, a special subset…

The equivalent binary parity check matrices for the binary images of the cycle-free non-binary LDPC codes have numerous bit-level cycles. In this paper, we show how to transform these binary parity check matrices into their cycle-free…

This paper demonstrates the use of neural networks for developing a system that can recognize hand-written English alphabets. In this system, each English alphabet is represented by binary values that are used as input to a simple feature…

In this paper, we examine a ciphertext on the basis of using geometrical objects. Each symbol normative alphabet is determined as a point on the plane. We consider possible ways for presentation of these points.

System-generated logs are typically converted into categorical log templates through parsing. These templates are crucial for generating actionable insights in various downstream tasks. However, existing parsers often fail to capture…

Rotation symmetric bosonic codes are an attractive encoding for qubits into oscillator degrees of freedom, particularly in superconducting qubit experiments. While these codes can tolerate considerable loss and dephasing, they will need to…

Consider a single-user or multiple-access channel with a large output alphabet. A method to approximate the channel by an upgraded version having a smaller output alphabet is presented and analyzed. The original channel is not necessarily…