Binary LCD Codes from ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$

Abstract

Linear complementary dual (LCD) codes over finite fields are linear codes satisfying $C\cap C^{\perp }=\{0\}$. We generalize the LCD codes over finite fields to ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$-LCD codes over the ring ${\mathbf{Z}}_2\times ({\mathbf{Z}}_2+u{\mathbf{Z}}_2)$. Under suitable conditions, ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$-linear codes that are ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$-LCD codes are characterized. We then prove that the binary image of a ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$-LCD code is a binary LCD code. Finally, by means of these conditions, we construct new binary LCD codes using ${\mathbb{Z}}_2{\mathbb{Z}}_2[u]$-LCD codes, most of which have better parameters than current binary LCD codes available.

arXiv admin note: text overlap with arXiv:1604.03774, arXiv:1705.00770, arXiv:1708.00997 by other authors

References in corpus (2)

• Linear codes over Fq which are equivalent to LCD codes
• Euclidean and Hermitian LCD MDS codes