학술논문
Constructions of large cyclic constant dimension codes via Sidon spaces.
Document Type
Journal
Author
Zhang, He (PRC-GUAN-SMI) AMS Author Profile; Tang, Chunming (PRC-GUAN-SMI) AMS Author Profile
Source
Subject
94 Information and communication, circuits -- 94B Theory of error-correcting codes and error-detecting codes
94B15Cyclic codes
94B15
Language
English
Abstract
The authors investigate Sidon spaces, which are subspaces of a finite vector space over a finite field. By investigating the orbits of different Sidon spaces, the authors give a construction for cyclic subspace codes of size $q^n-1$, where $q$ is the number of elements of the underlying finite field. These cyclic subspace codes have minimum distance ${2k-2}$, where $k$ is the dimension of the Sidon spaces (Theorem 3.8 and Theorem 3.9). In Theorem 3.13 the authors give a construction for a cyclic subspace code with minimum distance $2k$ and another one with greater minimum distance in Theorem 3.15.