PDF(225 KB)
An Analogue of the Z4-Goethals Code in Non-Primitive Length
ALAHMADI Adel,ALHAZMI Husain,ALI Shakir,HELLESETH Tor,HIJAZI Rola,LI Chunlei,SOL′E Patrick
Journal of Systems Science & Complexity ›› 2017, Vol. 30 ›› Issue (4) : 950-966.
PDF(225 KB)
PDF(225 KB)
An Analogue of the Z4-Goethals Code in Non-Primitive Length
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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