Connections between Linear Complementary Dual Codes, Permanents and Geometry

Adel N. Alahmadi, Husain S. Alhazmi, Hatoon Shoaib, David G. Glynn, Saeed Ur Rehman, Patrick Solé

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
43 Downloads (Pure)

Abstract

Linear codes with complementary duals, or LCD codes, have recently been applied to side-channel and fault injection attack-resistant cryptographic countermeasures. We explain that over characteristic two fields, they exist whenever the permanent of any generator matrix is non-zero. Alternatively, in the binary case, the matroid represented by the columns of the matrix has an odd number of bases. We explain how Grassmannian varieties as well as linear and quadratic complexes are connected with LCD codes. Accessing the classification of polarities, we relate the binary LCD codes of dimension k to the two kinds of symmetric non-singular binary matrices, to certain truncated Reed–Muller codes, and to the geometric codes of planes in finite projective space via the self-orthogonal codes of dimension k.

Original languageEnglish
Article number2774
Number of pages11
JournalMathematics
Volume11
Issue number12
DOIs
Publication statusPublished - 20 Jun 2023

Keywords

  • code
  • invariant
  • rectangular matrix
  • permanent
  • dual code
  • complementary code
  • geometric code
  • Reed-Muller
  • Grassmannian
  • polarity
  • self-orthogonal
  • matroid

Fingerprint

Dive into the research topics of 'Connections between Linear Complementary Dual Codes, Permanents and Geometry'. Together they form a unique fingerprint.

Cite this