Title: Codes with low-dimensional hull

Authors: Xiangrui Meng; Vidya Sagar; Ritumoni Sarma

Addresses: School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, China ' Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India ' Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India

Abstract: In this article, certain linear codes over a finite field are constructed using multiplicative characters of another finite field. We discuss certain sufficient conditions under which these are either LCD codes or linear codes with one-dimensional hull. General Gauss sums are used heavily to achieve these results. Each theorem proved in this paper, is supported by an example with the help of Magma software. Finally, we show that if the base field is of characteristic 2, these codes are isodual.

Keywords: linear code; hull; Gauss sum; isodual code.

DOI: 10.1504/IJICOT.2022.125828

International Journal of Information and Coding Theory, 2022 Vol.6 No.1, pp.71 - 86

Received: 22 Feb 2022
Accepted: 26 Jul 2022
Published online: 29 Sep 2022 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article