Cyclic subspace codes via subspace polynomials


Otal K. , ÖZBUDAK F.

DESIGNS CODES AND CRYPTOGRAPHY, vol.85, no.2, pp.191-204, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 85 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.1007/s10623-016-0297-1
  • Title of Journal : DESIGNS CODES AND CRYPTOGRAPHY
  • Page Numbers: pp.191-204
  • Keywords: Random network coding, Subspace codes, Constant dimension codes, Grassmannian, Cyclic subspace codes, Subspace polynomials

Abstract

Subspace codes have been intensely studied in the last decade due to their application in random network coding. In particular, cyclic subspace codes are very useful subspace codes with their efficient encoding and decoding algorithms. In a recent paper, Ben-Sasson et al. gave a systematic construction of subspace codes using subspace polynomials. In this paper, we mainly generalize and improve their result so that we can obtain larger codes for fixed parameters and also we can increase the density of some possible parameters. In addition, we give some relative remarks and explicit examples.