Z4-Linear Perfect Codes
Denis Krotov (Sobolev Institute of Mathematics, Novosibirsk, Russia)

TL;DR
This paper establishes the existence and classification of a specific family of $Z_4$-linear extended perfect codes with distance 4 for lengths that are powers of two greater than 8, highlighting their diversity in ranks.
Contribution
It proves the existence of exactly $[(k+1)/2]$ mutually nonequivalent $Z_4$-linear extended perfect codes for each applicable length and characterizes their ranks.
Findings
Number of such codes is exactly $[(k+1)/2]$ for each length.
All these codes have distinct ranks.
The codes exist for all lengths $n=2^k > 8$.
Abstract
For every there exist exactly mutually nonequivalent -linear extended perfect codes with distance 4. All these codes have different ranks.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research
