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Projective-Plane Iteratively Decodable Block Codes for WDM High-Speed Long-Haul Transmission Systems

I.B. Djordjevic, S. Sankaranarayanan, B.V. Vasic
2004 Journal of Lightwave Technology  
A cyclic or quasi-cyclic form of finite geometry LDPC codes simplifies the encoding procedure.  ...  In this paper, the authors consider LDPC codes from affine planes, projective planes, oval designs, and unitals.  ...  A finite affine plane of order , say AG(2, ), is a design, and is a power of prime. A finite affine plane of order , is a special case of a finite projective plane of the same order.  ... 
doi:10.1109/jlt.2004.825768 fatcat:jagramkivfbyllolygkvyp5ooa

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  
A. Munemasa and V.D. Tonchev, A new quasi-symmetric 2-(56,16,6) design obtained from codes Discrete Math. 284 (2004), 231-234. 56. V. D.  ...  Tonchev, Nonbinary quantum codes derived from finite geometries, Finite Fields Appl., 18 (2012), 63-69. 47. R. Fuji-Hara, A. Munemasa and V.D.  ... 
doi:10.1145/1529282.1529502 dblp:conf/sac/WangT09 fatcat:a22hnn2b2bandlxovu2sa3dgxy

An algorithm for optimal difference systems of sets

Vladimir D. Tonchev, Hao Wang
2007 Journal of combinatorial optimization  
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, Quantum Codes from Caps, Discrete Math. 2. V. D. Tonchev, Generalized weighing matrices and self-orthogonal codes, Discrete Math. 2008 3. V.D.  ...  On symmetric nets and generalized Hadamard matrices from affine designs, J. Geometry 67 (2000), 180-187 (with V. Mavron). 41.  ... 
doi:10.1007/s10878-007-9064-6 fatcat:zgfx2dhb6rabhkpjcfe3vbummy

Iteratively decodable codes on m flats for WDM high-speed long-haul transmission

S. Sankaranarayanan, I.B. Djordjevic, B. Vasic
2005 Journal of Lightwave Technology  
As a natural extension of the prior work, in this paper, we consider LDPC codes on m flats derived from projective and affine geometries, which outperform codes from finite planes.  ...  In an earlier paper, we reported that the low-density parity-check (LDPC) codes from finite planes outperform any other known forward error-correction (FEC) scheme for optical communications.  ...  Similarly, codes from finite geometries with rate ∼ 0.62 achieve a gain of 12 dB at a BER of 10 −9 .  ... 
doi:10.1109/jlt.2005.857736 fatcat:lko5gq2e2vbljgary6ptdox3ii

Page 8746 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
P. (4-SUSX-SM; Brighton) Complete systems of lines on a Hermitian surface over a finite field. (English summary) Des. Codes Cryptogr. 17 (1999), no. 1-3, 253-268.  ...  Prince, Flag- transitive affine planes of order at most 125 (208-216); Joseph A.  ... 

Page 2383 of Mathematical Reviews Vol. , Issue 93e [page]

1993 Mathematical Reviews  
It is the dual of the affine plane AG(2, 4), or the 2-(16, 4, 1) design. M is constructed from a set of 20 points arranged in 5 tetrads.  ...  (NL-EIND); Calderbank, A. R. (1-BELL-M) Quasi-symmetric designs and the Smith normal form. Des. Codes Cryptogr. 2 (1992), no.2, 189-206.  ... 

Page 2734 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
code by simultane- ous optimization of expressions (231-248); A.  ...  Fiol, On the order and size of s-geodetic digraphs with given connectiv- ity (19-27); Simeon Ball, On small complete arcs in a finite plane (29-34); Luigia Berardi, Marco Buratti and Stefano Innamorati  ... 

Page 3213 of Mathematical Reviews Vol. , Issue 92f [page]

1992 Mathematical Reviews  
Lunardon, A remark on the derivation of flocks (pp. 299-309); T. Maruta, A geometric ap- proach to semi-cyclic codes (pp. 311-318); G.  ...  Brown, Group partitions, affine spaces and translation groups (pp. 19-25); A. Blokhuis and F. Mazzocca, On maximal sets of nuclei in PG(2,q) and quasi- odd sets in AG(2,q) (pp. 27-34); A.  ... 

Page 4730 of Mathematical Reviews Vol. , Issue 97H [page]

1997 Mathematical Reviews  
Zieve, A family of exceptional polynomials in characteristic three (209-218); Wen-Ching Winnie Li, Estimates of character sums arising from finite upper half planes (219-228); Véronique Mauduit, Carmichael-Carlitz  ...  , Use characteristic sets to decode cyclic codes up to actual minimum distance (297-312); Igor Shparlinski [I.  ... 

A Geometrical Realisation of Quasi-Cyclic Codes [chapter]

Cristina Martinez Ramirez, Alberto Besana
2020 Probability, Combinatorics and Control  
Further, we study quasi-cyclic codes as orbit codes in the Grassmannian parameterizing constant dimension codes.  ...  We study and enumerate cyclic codes which include generalised Reed-Solomon codes as function field codes.  ...  Cyclic codes are function field codes constructed over the curve C n,m with affine equation y m þ x n ¼ 1 defined over a finite field  q of q elements, where q is a power of a prime p and n, m are integer  ... 
doi:10.5772/intechopen.88288 fatcat:l7k2pzf6c5ar7kezheqvp6dltu

Page 3882 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
of the finite simple groups.  ...  The codes were initially taken as cyclic codes of odd prime length p. A. M. Gleason and E.  ... 

Automorphisms and Encoding of AG and Order Domain Codes [chapter]

John B. Little
2009 Gröbner Bases, Coding, and Cryptography  
If a linear code C over F q has a finite abelian group H as a group of automorphisms, then C has the structure of a module over a polynomial ring P.  ...  We illustrate these observations with several examples including geometric Goppa codes and codes from order domains.  ...  Since it relies only on the presence of suitable groups of code automorphisms, it applies to many classes of codes, including cyclic, quasi-cyclic, abelian, and many Goppa-type evaluation codes from curves  ... 
doi:10.1007/978-3-540-93806-4_7 fatcat:nzs6cqo33baivdsv6zp6omamwa

Low-density parity-check codes for 40-gb/s optical transmission systems

I.B. Djordjevic, S. Sankaranarayanan, S.K. Chilappagari, B. Vasic
2006 IEEE Journal of Selected Topics in Quantum Electronics  
The second class is the turbo product codes with Bose-Chaudhuri-Hocquenghen component codes.  ...  The analysis in this paper shows that the LDPC codes perform better than the other codes in the waterfall region at bit error rates as low as 10 −9 .  ...  In this paper, we will restrict our analysis to codes from projective and affine planes.  ... 
doi:10.1109/jstqe.2006.876182 fatcat:tbcdw5dfcnedfmklgee73zave4

Designs and codes: An update

E.F. Assmus, J.D. Key
1996 Designs, Codes and Cryptography  
Since the publication in 1992 of "Designs and their Codes" significant progress has been made in the general area of codes coming from designs.  ...  Acknowledgments Both authors would like to thank René Peeters and John Dillon for a careful reading of an earlier draft of this article and saving us from blunders.  ...  Projective and affine planes Finite projective planes of order n are symmetric designs with parameters (n 2 + n + 1, n + 1, 1) and finite affine planes are designs with parameters 2-(n 2 , n, 1), where  ... 
doi:10.1007/bf00169770 fatcat:qrs2i6wlr5gkzb4vsncd4glsfi

Designs and Codes: An update [chapter]

E. F. Assmus, J. D. Key
1996 Codes, Designs and Geometry  
Since the publication in 1992 of "Designs and their Codes" significant progress has been made in the general area of codes coming from designs.  ...  Acknowledgments Both authors would like to thank René Peeters and John Dillon for a careful reading of an earlier draft of this article and saving us from blunders.  ...  Projective and affine planes Finite projective planes of order n are symmetric designs with parameters (n 2 + n + 1, n + 1, 1) and finite affine planes are designs with parameters 2-(n 2 , n, 1), where  ... 
doi:10.1007/978-1-4613-1423-3_1 fatcat:trpwyoxhabe73okfp3bun43ime
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