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17
The Nordstrom-Robinson code is the binary image of the octacode
- Proceedings DIMACS/IEEE Workshop on Coding and
, 1992
"... 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 ..."
Abstract
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Cited by 29 (7 self)
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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
Nordstrom-Robinson code and A_7-geometry
, 2004
"... The Nordstrom-Robinson code NR is a non-linear binary code of length 16, with 2^8 codewords and minimum distance 6. Its automorphism group is a semidirect product of an elementary abelian group of order 16 and the alternating group A_7 . This group and the corresponding action of A_7 is also at t ..."
Abstract
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Cited by 3 (2 self)
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The Nordstrom-Robinson code NR is a non-linear binary code of length 16, with 2^8 codewords and minimum distance 6. Its automorphism group is a semidirect product of an elementary abelian group of order 16 and the alternating group A_7 . This group and the corresponding action of A_7 is also
Some nonregular designs from the Nordstrom–Robinson code and their statistical properties
, 2005
"... ..."
Construction of a (64, 2 , 12) Code via Galois Rings
, 1997
"... Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock and Preparata codes, which exist for all lengths 4 16. At length 16 they coincide to give the Nordstrom-Robinson code. This paper constructs a nonlinear (64, 2 , 12) ..."
Abstract
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Cited by 2 (0 self)
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Certain nonlinear binary codes contain more codewords than any comparable linear code presently known. These include the Kerdock and Preparata codes, which exist for all lengths 4 16. At length 16 they coincide to give the Nordstrom-Robinson code. This paper constructs a nonlinear (64, 2 , 12
L Reed-Muller, Nordstrom-Robinson, or Hamming
"... Abstract-Let 8 be a code of length n over a field F, with automorphism group G; 8, denotes the subset of codewords of weight w. Our goal is to classify the vectors of IF " into orbits under G and to determine their distances from the various subcodes 8,. We do this for the first-order Reed-Mull ..."
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-Muller, Nordstrom-Robinson, and Hamming codes of length 16, the Golay and shortened Golay codes of lengths 22, 23, 24, and the ternary Golay code of length 12.
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
The Z_4-linearity of Kerdock, Preparata, Goethals, and related codes
, 2001
"... 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 ..."
Abstract
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Cited by 178 (15 self)
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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
unknown title
"... This paper proposes encoding and decoding for nonlinear product codes and investigates the performance of nonlinear product codes. The proposed nonlinear product codes are constructed as N-dimensional product codes where the constituent codes are nonlinear binary codes derived from the linear codes ..."
Abstract
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over higher order alphabets, for example, Preparata or Kerdock codes. The performance and the complexity of the proposed construction are evaluated using the well-known nonlinear Nordstrom-Robinson code, which is presented in the generalized array code format with a low complexity trellis. The proposed
LDPC-coded 16-dimensional modulation based on the Nordstrom-Robinson nonlinear block code
- OSA Conf. Laser Electro-Optics (CLEO), JTh2A.24
, 2015
"... Recent forward error correction (FEC) codes based on low-density parity-check (LDPC) codes have shown capacity-achieving performance in practice. To support various modulation formats in conjunction with LDPC codes, bit-interleaved coded modulation (BICM) has been widely used. To achieve better perf ..."
Abstract
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Cited by 1 (1 self)
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propose a new 16-dimensional (16D) modulation based on the Nordstrom-Robinson (NR) nonlinear code. The NR code is an optimal binary code, whose minimum Hamming distance is 6, whereas the best-known linear code (BKLC) has a minimum distance of 5. We optimize LDPC codes for BICM-ID with vari-ous HDM formats
Results 1 - 10
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