
Previous Article
A new almost perfect nonlinear function which is not quadratic
 AMC Home
 This Issue

Next Article
Common distance vectors between Costas arrays
Finding an asymptotically bad family of $q$th power residue codes
1.  The University of Texas at Austin, Mathematics Department, C1200, 1 University Station, Austin, TX, 78712, United States 
In this paper, we examine families of generalized binary quadratic residue codes, named $q$th power residue codes, where $q$ is a fixed odd prime, and find an asymptotically bad subfamily of these codes. For each prime $l$ we will construct a $q$th power residue code of length $p$ (determined by our choice of $l$ ) and minimal distance $d_p$, with the property that as $l$ approaches infinity, $p$ also tends towards infinity, and $\lim_{l to \infty} \frac{d_p}{p} = 0$.
[1] 
Nigel Boston, Jing Hao. The weight distribution of quasiquadratic residue codes. Advances in Mathematics of Communications, 2018, 12 (2) : 363385. doi: 10.3934/amc.2018023 
[2] 
Min Ye, Alexander Barg. Polar codes for distributed hierarchical source coding. Advances in Mathematics of Communications, 2015, 9 (1) : 87103. doi: 10.3934/amc.2015.9.87 
[3] 
Hai Q. Dinh, Hien D. T. Nguyen. On some classes of constacyclic codes over polynomial residue rings. Advances in Mathematics of Communications, 2012, 6 (2) : 175191. doi: 10.3934/amc.2012.6.175 
[4] 
Karim Samei, Arezoo Soufi. Quadratic residue codes over $\mathbb{F}_{p^r}+{u_1}\mathbb{F}_{p^r}+{u_2}\mathbb{F}_{p^r}+...+{u_t}\mathbb{F}_ {p^r}$. Advances in Mathematics of Communications, 2017, 11 (4) : 791804. doi: 10.3934/amc.2017058 
[5] 
Masaaki Harada. Note on the residue codes of selfdual $\mathbb{Z}_4$codes having large minimum Lee weights. Advances in Mathematics of Communications, 2016, 10 (4) : 695706. doi: 10.3934/amc.2016035 
[6] 
Carla Mascia, Giancarlo Rinaldo, Massimiliano Sala. Hilbert quasipolynomial for order domains and application to coding theory. Advances in Mathematics of Communications, 2018, 12 (2) : 287301. doi: 10.3934/amc.2018018 
[7] 
Rabah Amir, Igor V. Evstigneev. On Zermelo's theorem. Journal of Dynamics & Games, 2017, 4 (3) : 191194. doi: 10.3934/jdg.2017011 
[8] 
John Hubbard, Yulij Ilyashenko. A proof of Kolmogorov's theorem. Discrete & Continuous Dynamical Systems  A, 2004, 10 (1&2) : 367385. doi: 10.3934/dcds.2004.10.367 
[9] 
HahngYun Chu, SeHyun Ku, JongSuh Park. Conley's theorem for dispersive systems. Discrete & Continuous Dynamical Systems  S, 2015, 8 (2) : 313321. doi: 10.3934/dcdss.2015.8.313 
[10] 
Sergei Ivanov. On Helly's theorem in geodesic spaces. Electronic Research Announcements, 2014, 21: 109112. doi: 10.3934/era.2014.21.109 
[11] 
Anish Ghosh, Dubi Kelmer. A quantitative Oppenheim theorem for generic ternary quadratic forms. Journal of Modern Dynamics, 2018, 12: 18. doi: 10.3934/jmd.2018001 
[12] 
Gokhan Calis, O. Ozan Koyluoglu. Architectureaware coding for distributed storage: Repairable block failure resilient codes. Advances in Mathematics of Communications, 2018, 12 (3) : 465503. doi: 10.3934/amc.2018028 
[13] 
Fabio Cipriani, Gabriele Grillo. On the $l^p$ agmon's theory. Conference Publications, 1998, 1998 (Special) : 167176. doi: 10.3934/proc.1998.1998.167 
[14] 
V. Niţicâ. Journé's theorem for $C^{n,\omega}$ regularity. Discrete & Continuous Dynamical Systems  A, 2008, 22 (1&2) : 413425. doi: 10.3934/dcds.2008.22.413 
[15] 
Jacques Féjoz. On "Arnold's theorem" on the stability of the solar system. Discrete & Continuous Dynamical Systems  A, 2013, 33 (8) : 35553565. doi: 10.3934/dcds.2013.33.3555 
[16] 
Dmitry Kleinbock, Barak Weiss. Dirichlet's theorem on diophantine approximation and homogeneous flows. Journal of Modern Dynamics, 2008, 2 (1) : 4362. doi: 10.3934/jmd.2008.2.43 
[17] 
Lena Noethen, Sebastian Walcher. Tikhonov's theorem and quasisteady state. Discrete & Continuous Dynamical Systems  B, 2011, 16 (3) : 945961. doi: 10.3934/dcdsb.2011.16.945 
[18] 
Fatiha AlabauBoussouira, Piermarco Cannarsa. A constructive proof of Gibson's stability theorem. Discrete & Continuous Dynamical Systems  S, 2013, 6 (3) : 611617. doi: 10.3934/dcdss.2013.6.611 
[19] 
Koray Karabina, Edward Knapp, Alfred Menezes. Generalizations of Verheul's theorem to asymmetric pairings. Advances in Mathematics of Communications, 2013, 7 (1) : 103111. doi: 10.3934/amc.2013.7.103 
[20] 
Mateusz Krukowski. ArzelàAscoli's theorem in uniform spaces. Discrete & Continuous Dynamical Systems  B, 2018, 23 (1) : 283294. doi: 10.3934/dcdsb.2018020 
2018 Impact Factor: 0.879
Tools
Metrics
Other articles
by authors
[Back to Top]