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Equivalence of Hadamard matrices and pseudo-noise matrices

T. Bella, V. Olshevsky, L. Sakhnovich, Franklin T. Luk
2005 Advanced Signal Processing Algorithms, Architectures, and Implementations XV  
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

Carl Bracken
2009 Journal of combinatorial designs (Print)  
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]

Carl Bracken
2008 arXiv   pre-print
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  
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  
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

V.M. DaSilva, E.S. Sousa
1994 IEEE Journal on Selected Areas in Communications  
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

Vladimir D. Tonchev, Hao Wang
2007 Journal of combinatorial optimization  
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]

Vladimir D. Tonchev, Hao Wang
2006 Lecture Notes in Computer Science  
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  
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

I.B. Djordjevic
2009 IEEE Photonics Technology Letters  
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  
“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  
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

Po-Ning Chen, Hsuan-Yin Lin, Stefan M. Moser
2012 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
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

Carl Bracken, Yeow Meng Chee, Punarbasu Purkayastha
2012 2012 IEEE International Symposium on Information Theory Proceedings  
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

Hao Wang, Vladimir D. Tonchev
2009 Proceedings of the 2009 ACM symposium on Applied Computing - SAC '09  
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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