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Equivalence of Hadamard matrices and pseudo-noise matrices
2005
Advanced Signal Processing Algorithms, Architectures, and Implementations XV
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Several classes of structured matrices (e.g., the Hadamard-Sylvester matrices and the pseudo-noise matrices) are used in the design of error-correcting codes. ...
In this paper we show that the two above classes essentially coincide: the pseudo-noise matrices can be obtained from the Hadamard-Sylvester matrices by means of the row/column permutations. ...
Section 1 is the introduction, and herein we will present some basic ideas and definitions from the theory of error correcting codes. ...
doi:10.1117/12.623303
fatcat:6qtm5bkrzjae5emdj5ykympbdi
Pseudo quasi-3 designs and their applications to coding theory
2009
Journal of combinatorial designs (Print)
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Quasi-symmetric designs can be used to construct optimal self complementary codes. ...
In this article we give a construction of an infinite family of pseudo quasi-3 designs whose residual designs allow us to construct a family of codes with a new parameter set that meet the Grey Rankin ...
In [1] the infinite family of error correcting codes with parameters (2u 2 − u, 8u 2 , u 2 − u) were constructed using u × u Hadamard matrices. ...
doi:10.1002/jcd.20208
fatcat:m5w744ongnezlkz72hjfw5nm2e
Pseudo Quasi-3 Designs and their Applications to Coding Theory
[article]
2008
arXiv
pre-print
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Quasi-symmetric designs can be used to construct optimal self complementary codes. ...
In this article we give a construction of an infinite family of pseudo quasi-3 designs whose residual designs allow us to construct a family of codes with a new parameter set that meet the Grey Rankin ...
In [1] the infinite family of error correcting codes with parameters (2u 2 − u, 8u 2 , u 2 − u) were constructed using u × u Hadamard matrices. ...
arXiv:0804.1740v1
fatcat:xj6y36yqmfaifbn6y2jhatg6ca
Page 9450 of Mathematical Reviews Vol. , Issue 2002M
[page]
2002
Mathematical Reviews
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The majority of these classes arise from the dihedral-cocyclic Hadamard matrices. ...
There is also a class of dihedral-cocyclic Hadamard matrices which gives a large collection of [40,20] codes with only one codeword of length 4.”
2002m:94070 94B25 11T7! ...
Page 7945 of Mathematical Reviews Vol. , Issue 97M
[page]
1997
Mathematical Reviews
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Summary: “A construction of binary self-dual singly-even codes from Hadamard matrices is described. ...
As an application, all inequivalent extremal singly-even [40,20,8] codes derived from Hadamard matrices of order 20 are enumerated.”
{For the entire collection see MR 97k:68003.} ...
Multicarrier orthogonal CDMA signals for quasi-synchronous communication systems
1994
IEEE Journal on Selected Areas in Communications
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Orthogonal sequences based on the Sylvester-type Hadamard matrices (Walsh functions) are shown to provide a significant improvement over the case where a Hadamard (orthogonal) matrix is chosen at random ...
We search for sets of sequences that minimize the probability of symbol detection error, given that there is imperfect synchronization among the signals, that is, the signals are quasi-synchronous. ...
The current trend, especially in mobile communications, is to use forward error correction codes and to design the system to operate at a relatively large symbol error rate (e.g., and higher). ...
doi:10.1109/49.298058
fatcat:77dulov25jaopd23djp2xtrqqq
An algorithm for optimal difference systems of sets
2007
Journal of combinatorial optimization
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Tonchev, Quantum Codes from Caps, Discrete Math. 2. V. D. Tonchev, Generalized weighing matrices and self-orthogonal codes, Discrete Math. 2008 3. V.D. ...
Tonchev, Cyclic quasi-symmetric designs and self-orthogonal codes of length 63, J. Stat. Planning and Inference, 138 (2008), 80-85. 5. V.C. Mavron , T.P. McDonough, and V.D. Tonchev. ...
Tonchev, Error-correcting codes from graphs, Discrete Math. 26. D. Betten, A. Betten and V.D. Tonchev, Unitals and Codes, Discrete Math.267 (2003),
23-33.
2002
257 (2002), 549-
557.
29. D. ...
doi:10.1007/s10878-007-9064-6
fatcat:zgfx2dhb6rabhkpjcfe3vbummy
Optimal Difference Systems of Sets with Multipliers
[chapter]
2006
Lecture Notes in Computer Science
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Tonchev, Symmetric (4, 4)-nets and generalized Hadamard matrices over groups of order 4, Designs, Codes and Cryptography 34 (2005), 71-87. 7. M. Harada, A. Munemasa and V.D. ...
Tonchev, A Characterization of Designs Related to an Extremal Doubly-Even Self-Dual Code ...
Tonchev, Error-correcting codes from graphs, Discrete Math. Moscow, December 7-11, 2004, Moscow State University Press, Moscow 2004, pp. 242-
246 (in Russian).
11. A. Munemasa and V.D. ...
doi:10.1007/11753728_61
fatcat:xxc734q4ojetfct3fzquowbxwm
Page 4870 of Mathematical Reviews Vol. , Issue 2003f
[page]
2003
Mathematical Reviews
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For general error-correcting codes, the abridging cyclic codes can be constructed as follows. ...
Summary: “In this note, we investigate type I codes over Z4 con- structed from Hadamard matrices. As an application, we construct a Type I Z4-code with minimum Euclidean weight 16 of length 40. ...
Photonic Quantum Dual-Containing LDPC Encoders and Decoders
2009
IEEE Photonics Technology Letters
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We propose encoder and decoder architectures for quantum low-density parity-check (LDPC) codes suitable for all-optical implementation, based on controlled-NOT (CNOT) and Hadamard gates only. ...
In addition, we propose several quantum LDPC codes based on balanced incomplete block designs. ...
sparse -matrices require a small number of interactions per qubit to determine the error location, and 4) excellent error correction capabilities. ...
doi:10.1109/lpt.2009.2019262
fatcat:qsig37536vexfk64ybvytbhjeu
Page 4388 of Mathematical Reviews Vol. , Issue 86i
[page]
1986
Mathematical Reviews
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“In this paper we describe g-ary codes with minimal or quasi- minimal redundancy that correct errors, defects, and erasures of byte type. ...
Obviously, a q’-ary t-error-correcting (n,k)-code leads to a q-ary (nb, kb)-code that corrects any t errors of byte type. ...
Page 1440 of Mathematical Reviews Vol. , Issue 2001B
[page]
2001
Mathematical Reviews
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2001b:94035
94B Theory of error-correcting codes and error-detecting codes
2001b:94035 94B05
Bouyukliev, lliya (BG-AOS3-IMI; Veliko Tarnovo);
Jaffe, David B. (1-NE; Lincoln, NE);
Vavrek, Vesselin (BG-AOS3 ...
Summary: “We demonstrate that many well-known binary, qua- ternary, and q-ary codes are cocyclic Hadamard codes, that is, derived from a cocyclic generalized Hadamard matrix or its equiv- alents. ...
Weak flip codes and applications to optimal code design on the binary erasure channel
2012
2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
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Different from linear codes that only exist for a number of codewords M being an integer-power of 2, the fair weak flip code can be defined for an arbitrary M. ...
the error probability) among all linear or nonlinear codes for the binary erasure channel (BEC) for many values of the blocklength n and for M ≤ 6. ...
However, it is possible to find five (8, 7, 4) Hadamard codes that combine to a (8, 35, 20) fair weak flip code. ♦ Note that two Hadamard matrices can be equivalent if one can be obtained from the other ...
doi:10.1109/allerton.2012.6483213
dblp:conf/allerton/ChenLM12
fatcat:gv2mcxkhszgehgurlkxa3hoyty
Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices
2012
2012 IEEE International Symposium on Information Theory Proceedings
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In this article we construct an infinite family of linear error correcting codes over Fq for any prime power q. The code parameters are for any positive integer t. ...
Index Terms-Generalised Hadamard matrix, Grey-Rankin bound, q-ary codes. ...
These constructions use the structure of Hadamard matrices to obtain the quasi-symmetric designs and hence the codes. ...
doi:10.1109/isit.2012.6283038
dblp:conf/isit/BrackenCP12
fatcat:snbznffxvfevzmmko766mk63s4
An algorithm for optimal comma free codes with isomorphism rejection
2009
Proceedings of the 2009 ACM symposium on Applied Computing - SAC '09
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Tonchev, Error-correcting codes from graphs, Discrete Math. 257 (2002), 549-557. 63. D. Jungnickel and V.D. ...
On symmetric nets and generalized Hadamard matrices from affine designs, J. Geometry 67 (2000), 180-187 (with V. Mavron). 75. ...
doi:10.1145/1529282.1529502
dblp:conf/sac/WangT09
fatcat:a22hnn2b2bandlxovu2sa3dgxy
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