A characterization of two-weight projective cyclic codes
Tao Feng
TL;DR
This paper establishes necessary conditions for certain two-weight projective cyclic codes to decompose into specific subcodes, confirming a conjecture that all such codes are already known in the projective case.
Contribution
It provides a proof confirming Vega's conjecture that all two-weight projective cyclic codes of the specified type are among the known codes.
Findings
Necessary conditions for code decomposition are established.
Vega's conjecture is confirmed for the projective case.
The work aligns with previous research by Wolfmann and Vega.
Abstract
We give necessary conditions for a two-weight projective cyclic code to be the direct sum of two one-weight irreducible cyclic subcodes of the same dimension, following the work of Wolfmann and Vega. This confirms Vega's conjecture that all the two-weight cyclic codes of this type are the known ones in the projective case.
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