Optimal Self-Dual Z4-Codes and a Unimodular Lattice in Dimension 41
Masaaki Harada
TL;DR
This paper determines the maximum minimum Euclidean weight for Type I Z4-codes up to length 47 (excluding 37) and constructs the first explicit example of an optimal odd unimodular lattice in dimension 41 using such codes.
Contribution
It provides new bounds for Type I Z4-codes and presents the first explicit construction of an optimal odd unimodular lattice in dimension 41.
Findings
Maximum minimum Euclidean weight for lengths up to 47 (excluding 37)
Explicit construction of an optimal odd unimodular lattice in dimension 41
New bounds for Type I Z4-codes
Abstract
For lengths up to 47 except 37, we determine the largest minimum Euclidean weight among all Type I Z4-codes of that length. We also give the first example of an optimal odd unimodular lattice in dimension 41 explicitly, which is constructed from some Type I Z4-code of length 41.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cooperative Communication and Network Coding