A remark on full rank perfect codes
نویسندگان
چکیده
منابع مشابه
Full-Rank Perfect Codes over Finite Fields
In this paper, we propose a construction of fullrank q-ary 1-perfect codes over finite fields. This construction is a generalization of the Etzion and Vardy construction of fullrank binary 1-perfect codes (1994). Properties of i-components of q-ary Hamming codes are investigated and the construction of full-rank q-ary 1-perfect codes is based on these properties. The switching construction of 1...
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In wireless communication systems, space-time codes are applied to encode data when multiple antennas are used in the receiver and transmitter. The concept of diversity is very crucial in designing space-time codes. In this paper, using the equivalent definition of full diversity space-time codes, we first characterize all real and complex $2times 2$ rate one linear dispersion space-...
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The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-errorcorrecting binary code can be constructed by this combining construction is generalized to the q-ary case. Simply, every non-full-rank perfect code C is the union of a well-defined family of μ̄-components Kμ̄, where μ̄ belongs to an “outer” pe...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.02.014