In many massively parallel data management platforms, programs are represented as small imperative pieces of code connected in a data flow. This popular abstraction makes it hard to apply algebraic reordering techniques employed by relational DBMSs and other systems that use an algebraic programming abstraction. We present a code analysis technique based on reverse data and control flow analysi...

In this paper we introduce a new right preprocessing method for the decoding of 2 × 2 algebraic STBCs, called algebraic reduction, which exploits the multiplicative structure of the code. The principle of the new reduction is to absorb part of the channel into the code, by approximating the channel matrix with an element of the maximal order of the algebra. We prove that algebraic reduction att...

Høholdt, van Lint and Pellikaan proposed a generalization of one-point AG codes called the evaluation codes, and enabled us to construct linear codes from arbitrary algebraic varieties [5], [6]. To construct an evaluation code, we find an appropriate K-algebra R with an order function w and an epimorphism φ : R → Kn of K-algebras, where K is a finite field and n is the code length. Then we defi...

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems. Extended work has been done on single antenna fading channels, and algebraic lattice codes have been proven to be an effective tool. The general framework has been settled in the last ten years and many explicit cod...