The Nordstrom-Robinson code is algebraic-geometric
نویسندگان
چکیده
منابع مشابه
Nordstrom-Robinson code and A7-geometry
The Nordstrom-Robinson code NR is a non-linear binary code of length 16, with 2 codewords and minimum distance 6. Its automorphism group is a semidirect product of an elementary abelian group of order 16 and the alternating group A7. This group and the corresponding action of A7 is also at the origin of the sporadic A7-geometry. We construct this geometry and derive the Nordstrom-Robinson code ...
متن کاملThe Nordstrom-Robinson Code is the Binary Image of 19 the Octacode
The Nordstrom-Robinson code, a nonlinear binary code of length 16 and minimal Hamming distance 6, is the binary image of the octacode, a linear self-dual code over 4 of length 8 and minimal Lee distance 6. Since the octacode is the 4-analogue of a Hamming code, this provides an extremely simple definition of the Nordstrom-Robinson code. A different version of this paper appeared in: Coding and ...
متن کاملOn the extention of propelinear structures of Nordstrom-Robinson code to Hamming code
A code is called propelinear if its automorphism group contains a subgroup that acts regularly on its codewords, which is called a propelinear structure on the code. In the paper a classification of the propelinear structures on the Nordstrom-Robinson code is obtained and the question of extension of these structures to propelinear structures of the Hamming code, that contains the Nordstrom-Rob...
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Problem statement: Cryptosystem using linear codes was developed in 1978 by Mc-Eliece. Later in 1985 Niederreiter and others developed a modified version of cryptosystem using concepts of linear codes. But these systems were not used frequently because of its larger key size. In this study we were designing a cryptosystem using the concepts of algebraic geometric codes with smaller key size. Er...
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The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a construction method of such a selforthogonal space using an algebraic curve. By using the proposed method we construct an asymptotically good sequence of bina...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 1997
ISSN: 0018-9448
DOI: 10.1109/18.623154