On the ternary extended perfect Golay code by the modified GC-construction
DOI:
https://doi.org/10.55630/mem.2026.55.442-447Keywords:
the ternary extended perfect Golay code, modified generalised concatenation constructionAbstract
It is shown that the ternary extended perfect Golay [12, 6, 6]_3-code can be constructed by the modified GC-construction. For the binary Golay [24, 12, 8]-code this has been shown by us earlier. In particular, the Golay [12, 6, 6]_3-code can be constructed using the GC-construction with the inner codes of length 3 and the outer codes of length 4.
References
I. DUMER, V. ZINOVIEV, and V. ZYABLOV. Concatenated decoding according to minimal generalized distance. Problems of Control and Information Theory, 10(1):3–19, 1981.
F. J. MACWILLIAMS and N. J. A. SLOANE. The theory of Error Correcting Codes. North-Holland, 1986.
V. PLESS. On the uniqueness of the golay codes. J. Comb. Theory, 5:215–228, 1968.
V. ZINOVIEV, V. ZYABLOV, and N. VVEDENSKAYA. Comparizon of some algorithms of concatenated decoding. In Proc. of 8-th All-Union Conf. on Coding Theory and Inform. Transm. Pages 13–18, Moscow-Kuibyshev, 1981.
V. A. ZINOVIEV. Generalized concatenated codes. Problems of Information Transmission, 12(1):5–15, 1976.
V. A. ZINOVIEV and D. V. ZINOVIEV. On generalized concatenated construction of Nordstrom–Robinson code and binary Golay code. Problems of Information Transmission, 57(4):34–44, 2021.
V. A. ZINOVIEV and D. V. ZINOVIEV. On binary self-dual extremal double-even codes of length 80. Proc. Of Moscow Inst. Phys.-Tech., 14(2):85–94, 2022.
V. A. ZINOVIEV and V. V. ZYABLOV. Codes with unequal protection of information symbols. Problems of Information Transmission, 15(3):50–60, 1979.
V. A. ZINOVIEV and V. V. ZYABLOV. Correction of error bursts and independent errors using generalized concatenated codes. Problems of Information Transmission, 15(2):58–70, 1979.
