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Classification of Binary Self-Dual [48,24,10] Codes with an Automorphism of Odd Prime Order [article]

Stefka Bouyuklieva, Nikolay Yankov, Jon-Lark Kim
2012 arXiv   pre-print
The purpose of this paper is to complete the classification of binary self-dual [48,24,10] codes with an automorphism of odd prime order.  ...  By considering only an automorphism of type 3-(16,0), we prove that there are exactly 264 inequivalent self-dual [48, 24, 10] codes with an automorphism of odd prime order, equivalently, there are exactly  ...  no self-dual [48, 24, 10] codes with an automorphism of orders 5, 7, and 11.  ... 
arXiv:1201.4334v1 fatcat:ihhjneceo5fmlkiekczrnqqwna

Some optimal self-orthogonal and self-dual codes

Stefka Bouyuklieva
2004 Discrete Mathematics  
All optimal binary self-dual codes of lengths 42 and 44 which have an automorphism of order 5 with four independent cycles are obtained up to equivalence.  ...  All optimal self-dual codes of lengths 40, 42 and 44 which have an automorphism of order 3 with six independent cycles are constructed.  ...  Acknowledgements The author thanks Prof. Patric Östergård for checking the classification results for the self-orthogonal [n, k, 8] codes in Section 3.  ... 
doi:10.1016/j.disc.2004.06.010 fatcat:mu3boii54bhprpmgr6k4vm5ani

On the classification of binary self-dual [44,22,8] codes with an automorphism of order 3 or 7 [article]

Stefka Bouyuklieva, Nikolay Yankov, Radka Russeva
2011 arXiv   pre-print
All binary self-dual [44,22,8] codes with an automorphism of order 3 or 7 are classified.  ...  In this way we complete the classification of extremal self-dual codes of length 44 having an automorphism of odd prime order.  ...  Acknowledgements The authors would like to acknowledge the many helpful suggestions of the anonymous reviewers. We also thank the Editor of this Journal.  ... 
arXiv:1106.5960v1 fatcat:fhldb7eww5d5po7gflxizfpnc4

Construction of extremal self-dual codes over with an automorphism of odd order

Hyun Jin Kim, Yoonjin Lee
2012 Finite Fields and Their Applications  
We complete the classification the Lee-extremal self-dual codes over the ring F 2 + uF 2 of lengths 21 and 22 with a nontrivial automorphism of odd prime order except the case for an automorphism of order  ...  We use the decomposition theory for self-dual codes over F 2 + uF 2 with an automorphism of odd prime order as the same approaches made by Huffman.  ...  Acknowledgments We appreciate the referees' helpful comments, which improved the clarity of this paper.  ... 
doi:10.1016/j.ffa.2012.05.004 fatcat:elmoaxq3w5gmvout5axjioq6j4

Classification of binary self-dual [48,24,10] codes with an automorphism of odd prime order

Stefka Bouyuklieva, Nikolay Yankov, Jon-Lark Kim
2012 Finite Fields and Their Applications  
The purpose of this paper is to complete the classification of binary self-dual [48, 24, 10] codes with an automorphism of odd prime order.  ...  By considering only an automorphism of type 3-(16, 0), we prove that there are exactly 264 inequivalent self-dual [48, 24, 10] codes with an automorphism of odd prime order, equivalently, there are exactly  ...  Codes with an automorphism of odd prime order Codes with an automorphism of order 3 In this section we first classify self-dual codes with an automorphism of order 3.  ... 
doi:10.1016/j.ffa.2012.08.002 fatcat:3eoy64d4ibfm3ldnb4svre6noq

Self-dual codes over F2+uF2 with an automorphism of odd order

W. Cary Huffman
2009 Finite Fields and Their Applications  
Huffman, On the decomposition of self-dual codes over F 2 + uF 2 with an automorphism of odd prime order, Finite Fields Appl., in press].  ...  We complete the classification of all Lee-extremal and Lee-optimal self-dual codes over F 2 + uF 2 of lengths 9 through 20 that have a nontrivial odd order automorphism begun in [W.C.  ...  (i) Up to equivalence there are 4 Lee-extremal self-dual codes C with an automorphism of order 5 having 2 5-cycles.  ... 
doi:10.1016/j.ffa.2007.07.003 fatcat:q73dbbmapndg7nivbcfz3yrbru

Self-dual codes with an automorphism of order 13

Nikolay Yankov, Damyan Anev, Müberra Gürel
2017 Advances in Mathematics of Communications  
As for binary [80, 40] self-dual codes with an automorphism of type 13 − (6, 2) there are 162696 singly-even self-dual codes with minimum distance 14 and 195 doubly-even such codes with minimum distance  ...  Using a method for constructing binary self-dual codes having an automorphism of odd prime order p we classify, up to equivalence, all singlyeven self-dual [78, 39, 14] , [80, 40, 14] , [82, 41, 14] ,  ...  By Gilliver and Harada [8] there exist 5 extremal double circulant doubly-even self-dual codes of length 80 with an automorphism of order 13.  ... 
doi:10.3934/amc.2017047 fatcat:5f57chxlzrcibomejyopqc3kmq

Classification of binary self-dual [76, 38, 14] codes with an automorphism of order 9

Nikolay Yankov, Radka Russeva, Emine Karatash
2018 IEEE Transactions on Information Theory  
Using the method for constructing binary self-dual codes with an automorphism of order square of a prime number we have classified all binary self-dual codes with length 76 having minimum distance d=14  ...  Up to equivalence, there are six self-dual [76, 38, 14] codes with an automorphism of type 9-(8,0,4).  ...  The case for the length of an optimal binary self-dual code with automorphism of such order was considered by Yankov in [10] where it was proved that a doubly-even self-dual [72, 36, 16] codes with  ... 
doi:10.1109/tit.2018.2846564 fatcat:wqhocje73ffwfex473njometcq

Classification of the binary self-dual [42,21,8] codes having an automorphism of order 3

Stefka Bouyuklieva, Nikolay Yankov, Radka Russeva
2007 Finite Fields and Their Applications  
All optimal binary self-dual codes of length 42 which have an automorphism of order 3 are constructed.  ...  In this way we complete the classification of [42, 21, 8] SD codes having an automorphism of odd prime order.  ...  Acknowledgment Stefka Bouyuklieva is grateful to Magdeburg University for the excellent working conditions provided.  ... 
doi:10.1016/j.ffa.2006.01.001 fatcat:emgmvaslv5ek3e6jj4zqrbbl4q

A method for constructing self-dual codes with an automorphism of order 2

S. Bouyuklieva
2000 IEEE Transactions on Information Theory  
In this paper, we investigate binary self-dual codes with an automorphism of order 2 with cycles and fixed points.  ...  We prove that there do not exist self-dual [50 25 10] and [96 48 20] codes with an automorphism of order 2 with fixed points for 0 in their automorphism groups.  ...  A Method for Constructing Self-Dual Codes with an Automorphism of Order 2 Stefka Bouyuklieva Abstract-In this paper, we investigate binary self-dual codes with an automorphism of order 2 with cycles  ... 
doi:10.1109/18.825812 fatcat:fdey3rv7qveqxeqnd46qrm6dzu

Classification of Hadamard matrices of order 44 with automorphisms of order 7

Svetlana Topalova
2003 Discrete Mathematics  
The Hadamard matrices of order 44 possessing automorphisms of order 7 are classiÿed. The number of their equivalence classes is 384. The order of their full automorphism group is calculated.  ...  These Hadamard matrices yield 1683 nonisomorphic 3-(44,22,10) designs, 57932 nonisomorphic 2-(43,21,10) designs, and two inequivalent extremal binary self-dual doubly even codes of length 88 (one of them  ...  The ÿrst known extremal binary doubly even self-dual code of length 88 18 can be found using one of the 2-designs with an automorphism of order 43 (the one that was ÿrst constructed by Paley's theorem  ... 
doi:10.1016/s0012-365x(02)00400-4 fatcat:orbymsjunfbipeeo3b5iwlqxba

Self-Dual [24, 12, 8] Quaternary Codes with a Nontrivial Automorphism of Order 3

Radka Peneva Russeva
2002 Finite Fields and Their Applications  
All (Hermitian) self-dual [24, 12, 8] quaternary codes which have a non--trivial automorphism of order 3 are obtained up to equivalence. There exist exactly 205 inequivalent such codes.  ...  The codes under consideration are optimal, self-dual, and have the highest possible minimum distance for this length. 2002 Elsevier Science SELF-DUAL [24, 12, 8] QUATERNARY CODES  ...  The author is grateful to the anonymous referees for their comments.  ... 
doi:10.1006/ffta.2001.0322 fatcat:dnzyjguw7bglxmx64ikjuqmybe

Some new results on the self-dual [120,60,24] code [article]

Martino Borello, Javier de la Cruz
2017 arXiv   pre-print
The existence of an extremal self-dual binary linear code of length 120 is a long-standing open problem.  ...  Supposing the involutions acting fixed point freely, we show that also automorphisms of order 8 cannot occur and the automorphism group is of order at most 120, with further restrictions.  ...  Part of this work was done while he was in the University of Zurich supported by the Swiss Confederation through the Swiss Government Excellence Scholarship no. 2016.0873.  ... 
arXiv:1706.08114v2 fatcat:z2b2uvbrnjaoza7zs624la57wy

Classification of Quaternary Hermitian Self-Dual Codes of Length 20

Masaaki Harada, Akihiro Munemasa
2011 IEEE Transactions on Information Theory  
A classification of quaternary Hermitian self-dual codes of length 20 is given. Using this classification, a classification of extremal quaternary Hermitian self-dual codes of length 22 is also given.  ...  This work of the first author was supported by JST PRESTO program.  ...  The code with an automorphism group of order 1330560 is equivalent to the code C 22,P 1 in [8, Table 2 ], which is one of the three inequivalent pure double circulant extremal self-dual codes of length  ... 
doi:10.1109/tit.2011.2134330 fatcat:w3dod5e3grfejnjdtemdzfaepa

SELF-DUAL CODES AND FIXED-POINT-FREE PERMUTATIONS OF ORDER 2

Hyun Jin Kim
2014 Bulletin of the Korean Mathematical Society  
We construct new binary optimal self-dual codes of length 50. We develop a construction method for binary self-dual codes with a fixed-point-free automorphism of order 2.  ...  Using this method, we find new binary optimal self-dual codes of length 52. From these codes, we obtain Lee-optimal self-dual codes over the ring F 2 + uF 2 of lengths 25 and 26.  ...  For odd prime p, we find the construction method for a self-dual code of length 2n + 2 with an automorphism of order p with c independent cycles from a self-dual code of length 2n with an automorphism  ... 
doi:10.4134/bkms.2014.51.4.1175 fatcat:vz5zlg6x4zapda6lv5gr7xgkja
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