Skip to content

Research at St Andrews

4-codes and their Gray map images as orthogonal arrays

Research output: Contribution to journalArticlepeer-review

Author(s)

Peter Jephson Cameron, Josephine Kusuma, Patrick Solé

School/Research organisations

Abstract

A classic result of Delsarte connects the strength (as orthogonal array) of a linear code with the minimum weight of its dual: the former is one less than the latter.Since the paper of Hammons et al., there is a lot of interest in codes over rings, especially in codes over ℤ4 and their (usually non-linear) binary Gray map images.We show that Delsarte's observation extends to codes over arbitrary finite commutative rings with identity. Also, we show that the strength of the Gray map image of a ℤ4 code is one less than the minimum Lee weight of its Gray map image.
Close

Details

Original languageEnglish
Pages (from-to)109-114
JournalDesigns, Codes and Cryptography
Volume84
Issue number1-2
Early online date20 May 2016
DOIs
Publication statusPublished - Jul 2017

    Research areas

  • Commutative ring, Code, Lee weight, Orthogonal array, Gray map

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. The geometry of diagonal groups

    Bailey, R. A., Cameron, P. J., Praeger, C. E. & Schneider, C., 7 Jul 2021, (E-pub ahead of print) In: Transactions of the American Mathematical Society. Early View

    Research output: Contribution to journalArticlepeer-review

  2. Diagonal groups and arcs over groups

    Bailey, R. A., Cameron, P. J., Kinyon, M. & Praeger, C., 4 Jul 2021, (E-pub ahead of print) In: Designs, Codes and Cryptography. 11 p.

    Research output: Contribution to journalArticlepeer-review

  3. Forbidden subgraphs of power graphs

    Manna, P., Cameron, P. J. & Mehatari, R., 2 Jul 2021, In: Electronic Journal of Combinatorics. 28, 3, 14 p., P3.4.

    Research output: Contribution to journalArticlepeer-review

  4. Graphs defined on groups

    Cameron, P. J., 15 Apr 2021, (E-pub ahead of print) In: International Journal of Group Theory. In Press

    Research output: Contribution to journalArticlepeer-review

  5. Groups generated by derangements

    Bailey, R. A., Cameron, P. J., Giudici, M. & Royle, G. F., 15 Apr 2021, In: Journal of Algebra. 572, p. 245-262

    Research output: Contribution to journalArticlepeer-review

Related by journal

  1. Diagonal groups and arcs over groups

    Bailey, R. A., Cameron, P. J., Kinyon, M. & Praeger, C., 4 Jul 2021, (E-pub ahead of print) In: Designs, Codes and Cryptography. 11 p.

    Research output: Contribution to journalArticlepeer-review

  2. Near-complete external difference families

    Davis, J. A., Huczynska, S. & Mullen, G. L., Sep 2017, In: Designs, Codes and Cryptography. 84, 3, p. 415-424 10 p.

    Research output: Contribution to journalArticlepeer-review

  3. Equidistant frequency permutation arrays and related constant composition codes

    Huczynska, S., Feb 2010, In: Designs, Codes and Cryptography. 54, 2, p. 109-120 12 p.

    Research output: Contribution to journalArticlepeer-review

  4. A design and a geometry for the group Fi 22

    Cameron, P. J. & Rudvalis, A., 1 Sep 2007, In: Designs, Codes, and Cryptography. 44, 1-3, p. 11-14 4 p.

    Research output: Contribution to journalArticlepeer-review

ID: 242359707

Top