Related papers: Arithmetic Operators over Finite Field GF($2^m$) f…
Fault tolerance is a major concern in distributed computational settings. In the classic master-worker setting, a server (the master) needs to perform some heavy computation which it may distribute to $m$ other machines (workers) in order…
An efficient procedure for error-value calculations based on fast discrete Fourier transforms (DFT) in conjunction with Berlekamp-Massey-Sakata algorithm for a class of affine variety codes is proposed. Our procedure is achieved by…
Interval arithmetic libraries provide the four elementary arithmetic operators for operand intervals bounded by floating-point numbers. Actual implementations need to make a large case analysis that considers, e.g., magnitude relations…
Techniques that rigorously bound the overall rounding error exhibited by a numerical program are of significant interest for communities developing numerical software. However, there are few available tools today that can be used to…
A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…
We calculate a set of one-loop corrections to $h\to b\bar b$ and $h\to \tau\bar \tau$ decays in the dimension-6 Standard Model effective field theory (SMEFT). In particular, working in the limit of vanishing gauge couplings, we calculate…
Bicritical rational functions -- those with precisely two critical points -- include the well-studied families of unicritical polynomials and quadratic rational functions. In this article we lay out general foundations for studying…
We study subfield-subcodes of Generalized Toric (GT) codes over $\mathbb{F}_{p^s}$. These are the multidimensional analogues of BCH codes, which may be seen as subfield-subcodes of generalized Reed-Solomon codes. We identify polynomial…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
Finite field transforms are offered as a new tool of spreading sequence design. This approach exploits orthogonality properties of synchronous non-binary sequences defined over a complex finite field. It is promising for channels supporting…
The inherent uncertainty of communication channels implies that any coding scheme has a non-zero probability of failing to correct errors, making retransmission mechanisms essential. To ensure message reliability and integrity, a dual-layer…
Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…
In this paper, for the purposes of information transmission and network error correction simultaneously, three classes of important linear network codes in network coding, linear multicast/broadcast/dispersion codes are generalized to…
Here we present the cuLGT code for gauge fixing in lattice gauge field theories with graphic processing units (GPUs). Implementations for SU(3) Coulomb, Landau and maximally Abelian gauge fixing are available and the overrelaxation,…
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…
This paper considers fast algorithms for operations on linearized polynomials. We propose a new multiplication algorithm for skew polynomials (a generalization of linearized polynomials) which has sub-quadratic complexity in the polynomial…
Function-correcting codes (FCCs) protect specific function evaluations of a message against errors. This condition imposes a less stringent distance requirement than classical error-correcting codes (ECCs), allowing for reduced redundancy.…
We present optimized quantum circuits for GF$(2^m)$ multiplication and division operations, which are essential computing primitives in various quantum algorithms. Our ancilla-free GF multiplication circuit has the gate count complexity of…
Reed-Solomon (RS) codes are constructed over a finite field that have been widely employed in storage and communication systems. Many fast encoding/decoding algorithms such as fast Fourier transform (FFT) and modular approach are designed…