Results 11  20
of
32
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 Hammingdistance 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 ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
. The Kerdock and extended Preparata codes are something of an enigma in coding theory since they are both Hammingdistance 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
The Z_4linearity 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 NordstromRobinson, Kerdock, Preparata, Goethals, and DelsarteGoethals. It is shown here that all these codes can be very simply constructed as binary images under the ..."
Abstract

Cited by 178 (15 self)
 Add to MetaCart
Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by NordstromRobinson, Kerdock, Preparata, Goethals, and DelsarteGoethals. It is shown here that all these codes can be very simply constructed as binary images under
Many NonAbelian Groups Support Only Group Codes That Are Conformant To Abelian Group Codes. ISIT, 1997. Ulm. Germany. [5] Alexandr A. Nechaev. Kerdock code in a cyclic form
"... Abstract In this contribution we show the structure on some codes over nonAbelian groups, namely over D2m the dihedral group of 2 m elements. We use the polycyclic presentation of D2m to give a natural extension of Lee metric in this case and propose a structure theorem for such codes. Keywords Co ..."
Abstract
 Add to MetaCart
Abstract In this contribution we show the structure on some codes over nonAbelian groups, namely over D2m the dihedral group of 2 m elements. We use the polycyclic presentation of D2m to give a natural extension of Lee metric in this case and propose a structure theorem for such codes. Keywords
SpaceTime Signaling based on Kerdock and DelsarteGoethals Codes
 IEEE International Conference on Communications (ICC), pp 483  487
, 2004
"... Abstract — This paper designs spacetime codes for standard PSK and QAM signal constellations that have flexible rate, diversity and require no constellation expansion. Central to this construction are binary partitions of the PSK and QAM constellations that appear in codes designed for the Gaussian ..."
Abstract

Cited by 10 (6 self)
 Add to MetaCart
for the Gaussian channel. The spacetime codes presented here are designed by separately specifying the different levels of the binary partition in the spacetime array. The individual levels are addressed by either the binary symmetric matrices associated with codewords in a Kerdock code or other families
power, PAPR, PMPR,
, 1999
"... simplex code, dual BCH code, Kerdock code, DelsarteGoethals code, exponential ..."
Abstract
 Add to MetaCart
simplex code, dual BCH code, Kerdock code, DelsarteGoethals code, exponential
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 NordstromRobinson code is selfdual. 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

Cited by 15 (3 self)
 Add to MetaCart
codes are shown to be linear over Z4, the integers mod 4. The Kerdock and Preparata codes are duals over Z4, and the NordstromRobinson code is selfdual. All these codes are just extended cyclic codes over Z4. This provides a simple definition for these codes and explains why their Hamming weight
On the kernel and rank of Z4linear Preparatalike and Kerdocklike codes
, 2002
"... We say that a binary code of length n is additive if it is isomorphic to a subgroup of Z α 2 × Z β 4, where the quaternary coordinates are transformed to binary by means of the usual Gray map and hence α + 2β = n. In this paper we prove that any additive extended Preparatalike code always verifies ..."
Abstract
 Add to MetaCart
α = 0, i.e. it is always a Z4linear code. Moreover, we compute the rank and the dimension of the kernel of such Preparatalike codes and also the rank and the kernel of the Z4dual of these codes, i.e. the Z4linear Kerdocklike codes.
An Infinite Class of Counterexamples to a Conjecture Concerning NonLinear Resilient Functions
 Journal of Cryptology
, 1995
"... The main construction for resilient functions uses linear errorcorrecting codes; a resilient function constructed in this way is said to be linear. It has been conjectured that if there exists a resilient function, then there exists a linear function with the same parameters. In this note, we co ..."
Abstract

Cited by 24 (4 self)
 Add to MetaCart
construct infinite classes of nonlinear resilient functions from the Kerdock and Preparata codes. We also show that there do not exist linear resilient functions having the same parameters as the functions that we construct from the Kerdock codes. Thus, the aforementioned conjecture is disproved.
On Codes with Low PeaktoAverage Power Ratio for MultiCode CDMA
 Sequences and Their Applications, Discrete Mathematics and Theoretical Computer Science Series
, 2001
"... Codes which reduce the peaktoaverage power (PAPR) in multicode code division multiple access (MCCDMA) communications systems are systematically studied. The problem of designing such codes is reformulated as a new codingtheoretic problem: codes with low PAPR are ones in which the codewords are ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
are far from the firstorder ReedMuller code. Bounds on the tradeoff between rate, PAPR and errorcorrecting capability of codes for MCCDMA follow. The connections between the code design problem, bent functions and algebraic coding theory (in particular, the Kerdock codes and DelsarteGoethals codes
Results 11  20
of
32