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A new construction of two-, three- and few-weight codes via our GU codes and their applications

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Abstract

Linear codes with few weights have applications in cryptography, association schemes, designs, strongly regular graphs, finite group theory, finite geometries, and secret sharing schemes, among other disciplines. Two-weight linear codes are particularly interesting because they are closely related to objects in different areas of mathematics such as strongly regular graphs, 3-rank permutation groups, ovals, and arcs. There exist techniques to construct linear codes with few weights, for example, the systematic exposition by Calderbank and Kantor (Bull Lond Math Soc 18(2):97–122, 1986). Ding et al., (World Sci, pp 119–124, 2008) and (IEEE Trans Inf Theory 61(11):5835–5842, 2015) constructed few-weight codes using the trace function and Tonchev et al. (Algorithms, 12(8), 2019) generalized Ding’s construction. In this paper, we present an elementary way to get two- and three-weight codes from simplex codes and antipodal linear codes. An interesting application is the construction of uniformly packed linear codes from two-weight codes and quaternary quasi-perfect linear codes from three-weight codes.

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Authors and Affiliations

  1. Inter American University of Puerto Rico, San Juan, PR, 00957, USA

    Arrieta A Eddie

  2. University of Puerto Rico at Rio Piedras, San Juan, PR, 00925, USA

    Heeralal Janwa

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  1. Arrieta A Eddie
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  2. Heeralal Janwa
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Correspondence to Arrieta A Eddie.

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Eddie, A.A., Janwa, H. A new construction of two-, three- and few-weight codes via our GU codes and their applications. AAECC 33, 629–647 (2022). https://doi.org/10.1007/s00200-022-00561-8

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  • DOI: https://doi.org/10.1007/s00200-022-00561-8

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