CONSTRUCTION OF SELF-DUAL CODES OVER F2 + uF2

Title & Authors
CONSTRUCTION OF SELF-DUAL CODES OVER F2 + uF2
Han, Sung-Hyu; Lee, Hei-Sook; Lee, Yoon-Jin;

Abstract
We present two kinds of construction methods for self-dual codes over $\small{\mathbb{F}_2+u\mathbb{F}_2}$. Specially, the second construction (respectively, the first one) preserves the types of codes, that is, the constructed codes from Type II (respectively, Type IV) is also Type II (respectively, Type IV). Every Type II (respectively, Type IV) code over $\small{\mathbb{F}_2+u\mathbb{F}_2}$ of free rank larger than three (respectively, one) can be obtained via the second construction (respectively, the first one). Using these constructions, we update the information on self-dual codes over $\small{\mathbb{F}_2+u\mathbb{F}_2}$ of length 9 and 10, in terms of the highest minimum (Hamming, Lee, or Euclidean) weight and the number of inequivalent codes with the highest minimum weight.
Keywords
self-dual code;building-up construction;codes over ring;$\small{\mathbb{F}_2+u\mathbb{F}_2}$;
Language
English
Cited by
1.
AN EFFICIENT CONSTRUCTION OF SELF-DUAL CODES,;;

대한수학회보, 2015. vol.52. 3, pp.915-923
1.
A method for constructing self-dual codes over \$\$\mathbb {Z}_{2^m}\$\$ Z 2 m, Designs, Codes and Cryptography, 2015, 75, 2, 253
2.
Hermitian self-dual codes over, Finite Fields and Their Applications, 2014, 25, 106
3.
AN EFFICIENT CONSTRUCTION OF SELF-DUAL CODES, Bulletin of the Korean Mathematical Society, 2015, 52, 3, 915
4.
On the Problem of the Existence of a Square Matrix U Such That UUT=-I over Zpm, Information, 2017, 8, 3, 80
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