Abstract
This paper constructs a cyclic ℤ4-code with a parity-check matrix similar to that of Goethals code but in length 2m + 1, for all m ≥ 4. This code is a subcode of the lifted Zetterberg code for m even. Its minimum Lee weight is shown to be at least 10, in general, and exactly 12 in lengths 33, 65. The authors give an algebraic decoding algorithm which corrects five errors in these lengths for m = 5, 6 and four errors for m > 6.
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The work of Tor Helleseth and Chunlei Li was supported by the Norwegian Research Council.
This paper was recommended for publication by Editor DENG Yingpu.
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Alahmadi, A., Alhazmi, H., Ali, S. et al. An analogue of the ℤ4-Goethals code in non-primitive length. J Syst Sci Complex 30, 950–966 (2017). https://doi.org/10.1007/s11424-017-5244-3
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DOI: https://doi.org/10.1007/s11424-017-5244-3