Type IV-II codes over Z4 constructed from generalized bent functions

TL;DR

This paper introduces a new construction method for Type IV-II Z4-codes using generalized bent functions, leading to new self-dual binary codes with specific weight properties.

Contribution

It presents a novel construction of Type IV-II Z4-codes from generalized bent functions for odd lengths, extending them to self-dual binary codes via Gray map.

Findings

Constructed self-orthogonal Z4-codes of length 2^m for odd m

Extended these codes to Type IV-II Z4-codes for m ≥ 5

Derived self-dual Type II binary codes from the Z4-codes

Abstract

A Type IV-II Z4-code is a self-dual code over Z4 with the property that all Euclidean weights are divisible by eight and all codewords have even Hamming weight. In this paper we use generalized bent functions for a construction of self-orthogonal codes over Z4 of length $2^m$, for $m$ odd, $m \geq 3$, and prove that for $m \geq 5$ those codes can be extended to Type IV-II Z4-codes. From that family of Type IV-II Z4-codes, we obtain a family of self-dual Type II binary codes by using Gray map. We also consider the weight distributions of the obtained codes and the structure of the supports of the minimum weight codewords.