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28
ON DISTANCE NONREGULARITY OF PREPARATA CODES
"... Abstract: It is shown that among all Preparata codes only the code of length 16 is distance regular. An analogous result takes place for Preparata codes after puncturing any coordinate (only the code of length 15 is distance regular). ..."
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Abstract: It is shown that among all Preparata codes only the code of length 16 is distance regular. An analogous result takes place for Preparata codes after puncturing any coordinate (only the code of length 15 is distance regular).
Quantum Goethals-Preparata codes
, 2008
"... Abstract-We present a family of non-additive quantum codes based on Goethals and Preparata codes with parameters . The dimension of these codes is eight times higher than the dimension of the best known additive quantum codes of equal length and minimum distance. ..."
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Cited by 3 (1 self)
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Abstract-We present a family of non-additive quantum codes based on Goethals and Preparata codes with parameters . The dimension of these codes is eight times higher than the dimension of the best known additive quantum codes of equal length and minimum distance.
On weak isometries of Preparata codes
, 902
"... Let C1 and C2 be codes with code distance d. Codes C1 and C2 are called weakly isometric, if there exists a mapping J: C1 → C2, such that for any x, y from C1 the equality d(x, y) = d holds if and only if d(J(x), J(y)) = d. Obviously two codes are weakly isometric if and only if the minimal distan ..."
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distance graphs of these codes are isomorphic. In this paper we prove that Preparata code of length n ≥ 2 12 are weakly isometric if and only if these codes are equivalent. The analogous result is obtained for punctured Preparata codes of length not less than 2 10 − 1.
On the Apparent Duality of the Kerdock and Preparata Codes
, 1993
"... . The Kerdock and extended Preparata codes are something of an enigma in coding theory since they are both Hamming-distance invariant and have weight enumerators that are MacWilliams duals just as if they were dual linear codes. In this paper, we explain, by constructing in a natural way a Preparata ..."
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Cited by 6 (2 self)
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. The Kerdock and extended Preparata codes are something of an enigma in coding theory since they are both Hamming-distance invariant and have weight enumerators that are MacWilliams duals just as if they were dual linear codes. In this paper, we explain, by constructing in a natural way a
On the minimum distance graph of an extended Preparata code
, 2009
"... The minimum distance graph of an extended Preparata code P(m) has vertices corresponding to codewords and edges corresponding to pairs of codewords that are distance 6 apart. The clique structure of this graph is investigated and it is established that the minimum distance graphs of two extended Pre ..."
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The minimum distance graph of an extended Preparata code P(m) has vertices corresponding to codewords and edges corresponding to pairs of codewords that are distance 6 apart. The clique structure of this graph is investigated and it is established that the minimum distance graphs of two extended
CODING THEORY On Components of Preparata Codes
, 2003
"... Abstract—The paper considers the interrelation between i-components of an arbitrary Pre-parata-like code P and i-components of a perfect code C containing P. It is shown that each i-component of P can uniquely be completed to an i-component of C by adding a certain number of special codewords of C. ..."
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Abstract—The paper considers the interrelation between i-components of an arbitrary Pre-parata-like code P and i-components of a perfect code C containing P. It is shown that each i-component of P can uniquely be completed to an i-component of C by adding a certain number of special codewords of C
A linear construction for certain Kerdock and Preparata codes
- Bull. Amer. Math. Soc
, 1993
"... codes are shown to be linear over Z4, the integers mod 4. The Kerdock and Preparata codes are duals over Z4, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over Z4. This provides a simple definition for these codes and explains why their Hamming weight d ..."
Abstract
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Cited by 15 (3 self)
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codes are shown to be linear over Z4, the integers mod 4. The Kerdock and Preparata codes are duals over Z4, and the Nordstrom-Robinson code is self-dual. All these codes are just extended cyclic codes over Z4. This provides a simple definition for these codes and explains why their Hamming weight
Non-Additive Quantum Codes from Goethals and Preparata Codes
, 2008
"... We extend the stabilizer formalism to a class of nonadditive quantum codes which are constructed from non-linear classical codes. As an example, we present infinite families of nonadditive codes which are derived from Goethals and Preparata codes. ..."
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Cited by 5 (3 self)
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We extend the stabilizer formalism to a class of nonadditive quantum codes which are constructed from non-linear classical codes. As an example, we present infinite families of nonadditive codes which are derived from Goethals and Preparata codes.
Further Results on Generalized Hamming Weights for Goethals and Preparata Codes over
, 1999
"... This paper contains results on the generalized Hamming weights for the Goethals and Preparata codes over Z 4 : We give an upper bound on the rth generalized Hamming weights d r (m; j) for the Goethals code Gm (j) of length 2 m over Z 4 , when m is odd. We also determine d 3:5 (m; j) exactly. The ..."
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Cited by 4 (0 self)
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This paper contains results on the generalized Hamming weights for the Goethals and Preparata codes over Z 4 : We give an upper bound on the rth generalized Hamming weights d r (m; j) for the Goethals code Gm (j) of length 2 m over Z 4 , when m is odd. We also determine d 3:5 (m; j) exactly
A Family of Antipodal Distance-Regular Graphs Related to the Classical Preparata Codes
- Journal of Algebraic Combinatorics
, 1995
"... . A new family of distance-regular graphs is constructed. They are antipodal 2 2t\Gamma1 -fold covers of the complete graph on 2 2t vertices. The automorphism groups are determined, and the extended Preparata codes are reconstructed using walks on these graphs. There are connections to other int ..."
Abstract
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Cited by 9 (1 self)
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. A new family of distance-regular graphs is constructed. They are antipodal 2 2t\Gamma1 -fold covers of the complete graph on 2 2t vertices. The automorphism groups are determined, and the extended Preparata codes are reconstructed using walks on these graphs. There are connections to other
Results 1 - 10
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28
