Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable algebraic systems for being the base for such code generator. This work presents an attempt at realizing such idea in practice. A novel GA-based geometric code gene...

In this article, we present a new construction of codes from algebraic curves. Given a curve over a non-prime finite field, the obtained codes are defined over a subfield. We call them Cartier Codes since their construction involves the Cartier operator. This new class of codes can be regarded as a natural geometric generalisation of classical Goppa codes. In particular, we prove that a well-kn...

In this paper, the flow-field of an incompressible viscous flow past a solid-sphere at low Reynolds numbers (up to 270) is investigated numerically. In order to extend the capabilities of the finite volume method, the boundary (body) fitted coordinates (BFC) method is used. Transformation of the partial differential equations to algebraic relations is based on the finite-volume method with coll...

In this paper, the flow-field of an incompressible viscous flow past a solid-sphere at low Reynolds numbers (up to 270) is investigated numerically. In order to extend the capabilities of the finite volume method, the boundary (body) fitted coordinates (BFC) method is used. Transformation of the partial differential equations to algebraic relations is based on the finite-volume method with coll...

In this letter, a code-domain nonorthogonal multiple access (NOMA) technique based on an algebraic design is studied. We propose improved low-density spreading (LDS) sequence projective geometry. terms of its bit error rate (BER) performance, our proposed LDS code set outperforms the existing designs over frequency-nonselective Rayleigh fading and additive white Gaussian noise (AWGN) channels. ...

The order bound for the minimum distance of algebraic geometry codes was originally defined for the duals of one-point codes and later generalized for arbitrary algebraic geometry codes. Another bound of order type for the minimum distance of general linear codes, and for codes from order domains in particular, was given in [1]. Here we investigate in detail the application of that bound to one...

adder carry-lookahead, 131–133 full, 110, 129 half, 147 modulo-p, 524 ripple-carry, 130 serial-binary, 266–268 ternary, 148 admissible pattern, 189 algebraic divisor, 156, 234 double-cube, 234 multiple-cube, 234 single-cube, 234 algebraic factorization, 234–236, 247–250 targeted, 248 algebraic resubstitution, 234 aliasing, 463 alphabet code, 504–506 input, 270, 313, 414, 432, 441 output, 271, 4...

We introduce a group algebra formulation for bit optimal decoding of binary block codes. We use this new framework to give a simple algebraic proof that Pearl’s and Gallager’s belief propagation decoding algorithms are bit-optimal when the Tanner graph of the code is a tree. We believe that these derivations of known results give new insights into the issues of decoding on graphs from the algeb...

The LR parser generators that are bundled with many functional programming language implementations produce code that is untyped, needlessly inefficient, or both. We show that, using generalized algebraic data types, it is possible to produce parsers that are well-typed (so they cannot unexpectedly crash or fail) and nevertheless efficient. This is a pleasing result as well as an illustration o...

A plausible architecture of an ancient genetic code is derived from an extended base triplet vector space over the Galois field of the extended base alphabet {D,A,C,G,U}, where symbol D represents one or more hypothetical bases with unspecific pairings. We hypothesized that the high degeneration of a primeval genetic code with five bases and the gradual origin and improvement of a primeval DNA ...