Work

Ordered Orthogonal Array Construction Using LFSR Sequences

Year: 2016

Type: article

Abstract: We present a new construction of ordered orthogonal arrays (OOAs) of strength t with (q + 1)t columns over a finite field Fqusing linear feedback shift register sequences (LFSRs). OOAs are naturally related to (t, m, s)-nets, linear codes, and MDS codes. Our construction selects suitable columns from the array formed by all subintervals of length (qt-1)/(q-1) of an LFSR sequence generated by a primitive polynomial of degree t over Fq. We prove properties about the relative positions of runs in an LFSR, which guarantee that the constructed OOA has strength t. The set of parameters of our OOAs are the same as the ones given by Rosenbloom and Tsfasman (1997) and Skriganov (2002), but the constructed arrays are different. We experimentally verify that our OOAs are stronger than the Rosenbloom-Tsfasman-Skriganov OOAs in the sense that ours are “closer” to being a “full” orthogonal array. We also discuss how our OOA construction relates to previous techniques to build OOAs from a set of linearly independent vectors over Fq, as well as to hypergraph homomorphisms.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2016.2634010

Authors: Andre Guerino Castoldi, Lucia Moura, Daniel Panario, Brett Stevens

Institutions: Universidade Estadual de Maringá, Universidade Tecnológica Federal do Paraná, University of Ottawa, Carleton University

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: University of Ottawa, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Natural Sciences and Engineering Research Council of Canada, Ciência sem Fronteiras

Awards: G1164920944, G134464428, G905370527