Z4-linear codes obtained as projections of Kerdock and Delsarte-Goethals codes
نویسندگان
چکیده
منابع مشابه
The Z4-linearity of Kerdock, Preparata, Goethals, and related codes
Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson , Kerdock, Preparata, Goethals, and Delsarte-Goethals . It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over Z4, the integers mod 4 (although this requires a slight modificat...
متن کاملPD-sets for Z4-linear codes: Hadamard and Kerdock codes
Permutation decoding is a technique that strongly depends on the existence of a special subset, called PD-set, of the permutation automorphism group of a code. In this paper, a general criterion to obtain s-PD-sets of size s + 1, which enable correction up to s errors, for Z4-linear codes is provided. Furthermore, some explicit constructions of s-PD-sets of size s+1 for important families of (n...
متن کاملAssociation schemes related to Delsarte-Goethals codes
In this paper, we construct an infinite series of 9-class association schemes from a refinement of the partition of Delsarte-Goethals codes by their Lee weights. The explicit expressions of the dual schemes are determined through direct manipulations of complicated exponential sums. As a byproduct, the other three infinite families of association schemes are also obtained as fusion schemes and ...
متن کامل4 - Linearity of Kerdock , Preparata , Goethals and Related Codes ∗
Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson , Kerdock, Preparata, Goethals, and Delsarte-Goethals . It is shown here that all these codes can be very simply constructed as binary images under the Gray map of linear codes over 4, the integers mod 4 (although this requires a slight modificati...
متن کاملZ4-Linear Perfect Codes
For every n = 2 k ≥ 16 there exist exactly ⌊(k + 1)/2⌋ mutually nonequiv-alent Z 4-linear extended perfect codes with distance 4. All these codes have different ranks. Codes represented in such a manner are called Z 4-linear. In [5] it is shown that the extended Golay code and the extended Hamming (n, 2 n−log 2 n−1 , 4)-codes (of length n and cardinality 2 n−log 2 n−1 , with distance 4) for eve...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1995
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00239-n