-
Previous Article
New constructions of optimal frequency hopping sequences with new parameters
- AMC Home
- This Issue
-
Next Article
On dealer-free dynamic threshold schemes
Self-dual $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes with an automorphism of prime order
1. | Department of Mathematics and Statistics, Loyola University, Chicago, IL 60660, United States |
References:
[1] |
I. M. Araújo, et al., GAP reference manual,, The GAP Group, (). Google Scholar |
[2] |
J. Bierbrauer, Cyclic additive and quantum stabilizer codes,, in, (2007), 276.
|
[3] |
J. Bierbrauer and Y. Edel, Quantum twisted codes,, J. Combin. Des., 8 (2000), 174.
|
[4] |
S. Bouyuklieva and M. Harada, Extremal self-dual $[50,25,10]$ codes with automorphisms of order 3 and quasi-symmetric 2-$(49,9,6)$ designs,, Des. Codes Crypt., 28 (2003), 163.
doi: 10.1023/A:1022588407585. |
[5] |
S. Bouyuklieva, A. Malevich and W. Willems, Automorphisms of extremal self-dual codes,, IEEE Trans. Inform. Theory, IT-56 (2010), 2091.
|
[6] |
S. Bouyuklieva, N. Yankov and R. Russeva, Classification of the binary self-dual $[42,21,8]$ codes having an automorphism of order 3,, Finite Fields Appl., 13 (2007), 605.
doi: 10.1016/j.ffa.2006.01.001. |
[7] |
S. Bouyuklieva, N. Yankov and R. Russeva, On the classication of binary self-dual $[44,22,8]$ codes with an automorphism of order 3 or 7,, Int. J. Inform. Coding Theory, 2 (2011), 21.
|
[8] |
S. Buyuklieva and V. Yorgov, Singly-even self-dual codes of length 40,, Des. Codes Crypt., 9 (1996), 131.
|
[9] |
A. R. Calderbank, E. M. Rains, P. M. Shor and N. J. A. Sloane, Quantum error correction via codes over GF(4),, IEEE Trans. Inform. Theory, IT-44 (1998), 1369.
|
[10] |
L. E. Danielsen, Graph-based classification of self-dual additive codes over finite fields,, Adv. Math. Commun., 3 (2009), 329.
|
[11] |
L. E. Danielsen, On the classification of Hermitian self-dual additive codes over GF(9),, IEEE Trans. Inform. Theory, IT-58 (2012), 5500.
|
[12] |
B. K. Dey and B. S. Rajan, $\mathbb F_q$-linear cyclic codes over $\mathbb F_{q^m}$: DFT approach,, Des. Codes Crypt., 34 (2005), 89.
|
[13] |
R. Dontcheva and M. Harada, Extremal doubly-even $[80,40,16]$ codes with an automorphism of order 19,, Finite Fields Appl., 9 (2003), 157.
doi: 10.1016/S1071-5797(02)00018-7. |
[14] |
R. Dontcheva and M. Harada, Some extremal self-dual codes with an automorphism of order 7,, Appl. Algebra Engrg. Comm. Comput., 14 (2003), 75.
doi: 10.1007/s00200-003-0126-4. |
[15] |
W. C. Huffman, Automorphisms of codes with applications to extremal doubly even codes of length 48,, IEEE Trans. Inform. Theory, IT-28 (1982), 511.
|
[16] |
W. C. Huffman, On extremal self-dual quaternary codes of lengths 18 to 28 I,, IEEE Trans. Inform. Theory, IT-36 (1990), 651.
|
[17] |
W. C. Huffman, On extremal self-dual quaternary codes of lengths 18 to 28 II,, IEEE Trans. Inform. Theory, IT-37 (1991), 1206.
|
[18] |
W. C. Huffman, On extremal self-dual ternary codes of lengths 28 to 40,, IEEE Trans. Inform. Theory, IT-38 (1992), 1395.
|
[19] |
W. C. Huffman, Decompositions and extremal type II codes over $\mathbb Z_4$,, IEEE Trans. Inform. Theory, IT-44 (1998), 800.
|
[20] |
W. C. Huffman, Additive self-dual codes over $\mathbb F_4$ with an automorphism of odd prime order,, Adv. Math. Commun., 1 (2007), 357.
|
[21] |
W. C. Huffman, Additive cyclic codes over $\mathbb F_4$,, Adv. Math. Commun., 1 (2007), 429.
|
[22] |
W. C. Huffman, On the decomposition of self-dual codes over $\mathbb F_2 + u\mathbb F_2$ with an automorphism of odd prime order,, Finite Fields Appl., 13 (2007), 681.
doi: 10.1016/j.ffa.2006.02.003. |
[23] |
W. C. Huffman, Additive cyclic codes over $\mathbb F_4$ of even length,, Adv. Math. Commun., 2 (2008), 309.
|
[24] |
W. C. Huffman, Cyclic $\mathbb F_q$-linear $\mathbb F_{q^t}$-codes,, Int. J. Inform. Coding Theory, 1 (2010), 249.
|
[25] |
W. C. Huffman and V. D. Tonchev, The existence of extremal self-dual $[50,25,10]$ codes and quasi-symmetric 2-$(49,9,6)$ designs,, Des. Codes Crypt., 6 (1995), 97.
doi: 10.1007/BF01398008. |
[26] |
W. C. Huffman and V. D. Tonchev, The $[52,26,10]$ binary self-dual codes with an automorphism of order 7,, Finite Fields Appl., 7 (2001), 341.
doi: 10.1006/ffta.2000.0295. |
[27] |
V. I. Iorgov, Binary self-dual codes with automorphisms of odd order,, Problems Inform. Trans., 19 (1983), 260.
|
[28] |
V. I. Iorgov, Doubly even extremal codes of length 64,, Problems Inform. Trans., 22 (1986), 277.
|
[29] |
J.-L. Kim and J. Walker, Nonbinary quantum error-correcting codes from algebraic curves,, Discrete Math., 308 (2008), 3115.
|
[30] |
E. M. Rains, Nonbinary quantum codes,, IEEE Trans. Inform. Theory, IT-45 (1999), 1827.
|
[31] |
R. P. Russeva, Self-dual $[24,12,8]$ quaternary codes with a nontrivial automorphism of order 3,, Finite Fields Appl., 8 (2002), 34.
doi: 10.1006/ffta.2001.0322. |
[32] |
N. Yankov and R. Russeva, Binary self-dual codes of lengths 52 to 60 with an automorphism of order 7 or 13,, IEEE Trans. Inform. Theory, IT-57 (2011), 7498.
|
[33] |
V. Y. Yorgov, A method for constructing inequivalent self-dual codes with applications to length 56,, IEEE Trans. Inform. Theory, IT-33 (1987), 77.
|
[34] |
V. Y. Yorgov, The extremal codes of length 42 with an automorphism of order 7,, Discrete Math., 190 (1998), 201.
|
[35] |
V. Y. Yorgov and N. Ziapov, Doubly even self-dual $[40,20,8]$ codes with automorphism of an odd order,, Problems Inform. Trans., 32 (1996), 253.
|
show all references
References:
[1] |
I. M. Araújo, et al., GAP reference manual,, The GAP Group, (). Google Scholar |
[2] |
J. Bierbrauer, Cyclic additive and quantum stabilizer codes,, in, (2007), 276.
|
[3] |
J. Bierbrauer and Y. Edel, Quantum twisted codes,, J. Combin. Des., 8 (2000), 174.
|
[4] |
S. Bouyuklieva and M. Harada, Extremal self-dual $[50,25,10]$ codes with automorphisms of order 3 and quasi-symmetric 2-$(49,9,6)$ designs,, Des. Codes Crypt., 28 (2003), 163.
doi: 10.1023/A:1022588407585. |
[5] |
S. Bouyuklieva, A. Malevich and W. Willems, Automorphisms of extremal self-dual codes,, IEEE Trans. Inform. Theory, IT-56 (2010), 2091.
|
[6] |
S. Bouyuklieva, N. Yankov and R. Russeva, Classification of the binary self-dual $[42,21,8]$ codes having an automorphism of order 3,, Finite Fields Appl., 13 (2007), 605.
doi: 10.1016/j.ffa.2006.01.001. |
[7] |
S. Bouyuklieva, N. Yankov and R. Russeva, On the classication of binary self-dual $[44,22,8]$ codes with an automorphism of order 3 or 7,, Int. J. Inform. Coding Theory, 2 (2011), 21.
|
[8] |
S. Buyuklieva and V. Yorgov, Singly-even self-dual codes of length 40,, Des. Codes Crypt., 9 (1996), 131.
|
[9] |
A. R. Calderbank, E. M. Rains, P. M. Shor and N. J. A. Sloane, Quantum error correction via codes over GF(4),, IEEE Trans. Inform. Theory, IT-44 (1998), 1369.
|
[10] |
L. E. Danielsen, Graph-based classification of self-dual additive codes over finite fields,, Adv. Math. Commun., 3 (2009), 329.
|
[11] |
L. E. Danielsen, On the classification of Hermitian self-dual additive codes over GF(9),, IEEE Trans. Inform. Theory, IT-58 (2012), 5500.
|
[12] |
B. K. Dey and B. S. Rajan, $\mathbb F_q$-linear cyclic codes over $\mathbb F_{q^m}$: DFT approach,, Des. Codes Crypt., 34 (2005), 89.
|
[13] |
R. Dontcheva and M. Harada, Extremal doubly-even $[80,40,16]$ codes with an automorphism of order 19,, Finite Fields Appl., 9 (2003), 157.
doi: 10.1016/S1071-5797(02)00018-7. |
[14] |
R. Dontcheva and M. Harada, Some extremal self-dual codes with an automorphism of order 7,, Appl. Algebra Engrg. Comm. Comput., 14 (2003), 75.
doi: 10.1007/s00200-003-0126-4. |
[15] |
W. C. Huffman, Automorphisms of codes with applications to extremal doubly even codes of length 48,, IEEE Trans. Inform. Theory, IT-28 (1982), 511.
|
[16] |
W. C. Huffman, On extremal self-dual quaternary codes of lengths 18 to 28 I,, IEEE Trans. Inform. Theory, IT-36 (1990), 651.
|
[17] |
W. C. Huffman, On extremal self-dual quaternary codes of lengths 18 to 28 II,, IEEE Trans. Inform. Theory, IT-37 (1991), 1206.
|
[18] |
W. C. Huffman, On extremal self-dual ternary codes of lengths 28 to 40,, IEEE Trans. Inform. Theory, IT-38 (1992), 1395.
|
[19] |
W. C. Huffman, Decompositions and extremal type II codes over $\mathbb Z_4$,, IEEE Trans. Inform. Theory, IT-44 (1998), 800.
|
[20] |
W. C. Huffman, Additive self-dual codes over $\mathbb F_4$ with an automorphism of odd prime order,, Adv. Math. Commun., 1 (2007), 357.
|
[21] |
W. C. Huffman, Additive cyclic codes over $\mathbb F_4$,, Adv. Math. Commun., 1 (2007), 429.
|
[22] |
W. C. Huffman, On the decomposition of self-dual codes over $\mathbb F_2 + u\mathbb F_2$ with an automorphism of odd prime order,, Finite Fields Appl., 13 (2007), 681.
doi: 10.1016/j.ffa.2006.02.003. |
[23] |
W. C. Huffman, Additive cyclic codes over $\mathbb F_4$ of even length,, Adv. Math. Commun., 2 (2008), 309.
|
[24] |
W. C. Huffman, Cyclic $\mathbb F_q$-linear $\mathbb F_{q^t}$-codes,, Int. J. Inform. Coding Theory, 1 (2010), 249.
|
[25] |
W. C. Huffman and V. D. Tonchev, The existence of extremal self-dual $[50,25,10]$ codes and quasi-symmetric 2-$(49,9,6)$ designs,, Des. Codes Crypt., 6 (1995), 97.
doi: 10.1007/BF01398008. |
[26] |
W. C. Huffman and V. D. Tonchev, The $[52,26,10]$ binary self-dual codes with an automorphism of order 7,, Finite Fields Appl., 7 (2001), 341.
doi: 10.1006/ffta.2000.0295. |
[27] |
V. I. Iorgov, Binary self-dual codes with automorphisms of odd order,, Problems Inform. Trans., 19 (1983), 260.
|
[28] |
V. I. Iorgov, Doubly even extremal codes of length 64,, Problems Inform. Trans., 22 (1986), 277.
|
[29] |
J.-L. Kim and J. Walker, Nonbinary quantum error-correcting codes from algebraic curves,, Discrete Math., 308 (2008), 3115.
|
[30] |
E. M. Rains, Nonbinary quantum codes,, IEEE Trans. Inform. Theory, IT-45 (1999), 1827.
|
[31] |
R. P. Russeva, Self-dual $[24,12,8]$ quaternary codes with a nontrivial automorphism of order 3,, Finite Fields Appl., 8 (2002), 34.
doi: 10.1006/ffta.2001.0322. |
[32] |
N. Yankov and R. Russeva, Binary self-dual codes of lengths 52 to 60 with an automorphism of order 7 or 13,, IEEE Trans. Inform. Theory, IT-57 (2011), 7498.
|
[33] |
V. Y. Yorgov, A method for constructing inequivalent self-dual codes with applications to length 56,, IEEE Trans. Inform. Theory, IT-33 (1987), 77.
|
[34] |
V. Y. Yorgov, The extremal codes of length 42 with an automorphism of order 7,, Discrete Math., 190 (1998), 201.
|
[35] |
V. Y. Yorgov and N. Ziapov, Doubly even self-dual $[40,20,8]$ codes with automorphism of an odd order,, Problems Inform. Trans., 32 (1996), 253.
|
[1] |
Hongwei Liu, Jingge Liu. On $ \sigma $-self-orthogonal constacyclic codes over $ \mathbb F_{p^m}+u\mathbb F_{p^m} $. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020127 |
[2] |
Xiangrui Meng, Jian Gao. Complete weight enumerator of torsion codes. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020124 |
[3] |
Agnaldo José Ferrari, Tatiana Miguel Rodrigues de Souza. Rotated $ A_n $-lattice codes of full diversity. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020118 |
[4] |
Vito Napolitano, Ferdinando Zullo. Codes with few weights arising from linear sets. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020129 |
[5] |
Dandan Wang, Xiwang Cao, Gaojun Luo. A class of linear codes and their complete weight enumerators. Advances in Mathematics of Communications, 2021, 15 (1) : 73-97. doi: 10.3934/amc.2020044 |
[6] |
San Ling, Buket Özkaya. New bounds on the minimum distance of cyclic codes. Advances in Mathematics of Communications, 2021, 15 (1) : 1-8. doi: 10.3934/amc.2020038 |
[7] |
Shudi Yang, Xiangli Kong, Xueying Shi. Complete weight enumerators of a class of linear codes over finite fields. Advances in Mathematics of Communications, 2021, 15 (1) : 99-112. doi: 10.3934/amc.2020045 |
[8] |
Karan Khathuria, Joachim Rosenthal, Violetta Weger. Encryption scheme based on expanded Reed-Solomon codes. Advances in Mathematics of Communications, 2021, 15 (2) : 207-218. doi: 10.3934/amc.2020053 |
[9] |
Nicola Pace, Angelo Sonnino. On the existence of PD-sets: Algorithms arising from automorphism groups of codes. Advances in Mathematics of Communications, 2021, 15 (2) : 267-277. doi: 10.3934/amc.2020065 |
[10] |
Jong Yoon Hyun, Boran Kim, Minwon Na. Construction of minimal linear codes from multi-variable functions. Advances in Mathematics of Communications, 2021, 15 (2) : 227-240. doi: 10.3934/amc.2020055 |
[11] |
Sabira El Khalfaoui, Gábor P. Nagy. On the dimension of the subfield subcodes of 1-point Hermitian codes. Advances in Mathematics of Communications, 2021, 15 (2) : 219-226. doi: 10.3934/amc.2020054 |
[12] |
Shanding Xu, Longjiang Qu, Xiwang Cao. Three classes of partitioned difference families and their optimal constant composition codes. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020120 |
[13] |
Fengwei Li, Qin Yue, Xiaoming Sun. The values of two classes of Gaussian periods in index 2 case and weight distributions of linear codes. Advances in Mathematics of Communications, 2021, 15 (1) : 131-153. doi: 10.3934/amc.2020049 |
[14] |
Hongming Ru, Chunming Tang, Yanfeng Qi, Yuxiao Deng. A construction of $ p $-ary linear codes with two or three weights. Advances in Mathematics of Communications, 2021, 15 (1) : 9-22. doi: 10.3934/amc.2020039 |
[15] |
Tingting Wu, Li Liu, Lanqiang Li, Shixin Zhu. Repeated-root constacyclic codes of length $ 6lp^s $. Advances in Mathematics of Communications, 2021, 15 (1) : 167-189. doi: 10.3934/amc.2020051 |
[16] |
Saadoun Mahmoudi, Karim Samei. Codes over $ \frak m $-adic completion rings. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020122 |
[17] |
Ivan Bailera, Joaquim Borges, Josep Rifà. On Hadamard full propelinear codes with associated group $ C_{2t}\times C_2 $. Advances in Mathematics of Communications, 2021, 15 (1) : 35-54. doi: 10.3934/amc.2020041 |
[18] |
Yuan Cao, Yonglin Cao, Hai Q. Dinh, Ramakrishna Bandi, Fang-Wei Fu. An explicit representation and enumeration for negacyclic codes of length $ 2^kn $ over $ \mathbb{Z}_4+u\mathbb{Z}_4 $. Advances in Mathematics of Communications, 2021, 15 (2) : 291-309. doi: 10.3934/amc.2020067 |
[19] |
Hai Q. Dinh, Bac T. Nguyen, Paravee Maneejuk. Constacyclic codes of length $ 8p^s $ over $ \mathbb F_{p^m} + u\mathbb F_{p^m} $. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020123 |
[20] |
Kengo Matsumoto. $ C^* $-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms. Electronic Research Archive, , () : -. doi: 10.3934/era.2021006 |
2019 Impact Factor: 0.734
Tools
Metrics
Other articles
by authors
[Back to Top]