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On the generalization of the Costas property in the continuum
The equivalence of spacetime codes and codes defined over finite fields and Galois rings
1.  Department of Mathematics, University of Colorado at Boulder, Boulder, CO 803090395 
2.  Department of Electrical and Computer Engineering, University of Colorado at Boulder, Boulder, CO 803090425, United States 
[1] 
David Grant, Mahesh K. Varanasi. Duality theory for spacetime codes over finite fields. Advances in Mathematics of Communications, 2008, 2 (1) : 3554. doi: 10.3934/amc.2008.2.35 
[2] 
Hassan Khodaiemehr, Dariush Kiani. Highrate spacetime block codes from twisted Laurent series rings. Advances in Mathematics of Communications, 2015, 9 (3) : 255275. doi: 10.3934/amc.2015.9.255 
[3] 
Vincent Astier, Thomas Unger. Galois extensions, positive involutions and an application to unitary spacetime coding. Advances in Mathematics of Communications, 2019, 13 (3) : 513516. doi: 10.3934/amc.2019032 
[4] 
Delphine Boucher, Patrick Solé, Felix Ulmer. Skew constacyclic codes over Galois rings. Advances in Mathematics of Communications, 2008, 2 (3) : 273292. doi: 10.3934/amc.2008.2.273 
[5] 
Susanne Pumplün, Thomas Unger. Spacetime block codes from nonassociative division algebras. Advances in Mathematics of Communications, 2011, 5 (3) : 449471. doi: 10.3934/amc.2011.5.449 
[6] 
Frédérique Oggier, B. A. Sethuraman. Quotients of orders in cyclic algebras and spacetime codes. Advances in Mathematics of Communications, 2013, 7 (4) : 441461. doi: 10.3934/amc.2013.7.441 
[7] 
Grégory Berhuy. Algebraic spacetime codes based on division algebras with a unitary involution. Advances in Mathematics of Communications, 2014, 8 (2) : 167189. doi: 10.3934/amc.2014.8.167 
[8] 
Sergio R. LópezPermouth, Steve Szabo. On the Hamming weight of repeated root cyclic and negacyclic codes over Galois rings. Advances in Mathematics of Communications, 2009, 3 (4) : 409420. doi: 10.3934/amc.2009.3.409 
[9] 
Minjia Shi, Daitao Huang, Lin Sok, Patrick Solé. Double circulant selfdual and LCD codes over Galois rings. Advances in Mathematics of Communications, 2019, 13 (1) : 171183. doi: 10.3934/amc.2019011 
[10] 
Igor E. Shparlinski. On some dynamical systems in finite fields and residue rings. Discrete & Continuous Dynamical Systems  A, 2007, 17 (4) : 901917. doi: 10.3934/dcds.2007.17.901 
[11] 
Susanne Pumplün, Andrew Steele. The nonassociative algebras used to build fastdecodable spacetime block codes. Advances in Mathematics of Communications, 2015, 9 (4) : 449469. doi: 10.3934/amc.2015.9.449 
[12] 
Susanne Pumplün. How to obtain division algebras used for fastdecodable spacetime block codes. Advances in Mathematics of Communications, 2014, 8 (3) : 323342. doi: 10.3934/amc.2014.8.323 
[13] 
Aicha Batoul, Kenza Guenda, T. Aaron Gulliver. Some constacyclic codes over finite chain rings. Advances in Mathematics of Communications, 2016, 10 (4) : 683694. doi: 10.3934/amc.2016034 
[14] 
Somphong Jitman, San Ling, Patanee Udomkavanich. Skew constacyclic codes over finite chain rings. Advances in Mathematics of Communications, 2012, 6 (1) : 3963. doi: 10.3934/amc.2012.6.39 
[15] 
Eimear Byrne. On the weight distribution of codes over finite rings. Advances in Mathematics of Communications, 2011, 5 (2) : 395406. doi: 10.3934/amc.2011.5.395 
[16] 
Georgios T. Kossioris, Georgios E. Zouraris. Finite element approximations for a linear CahnHilliardCook equation driven by the space derivative of a spacetime white noise. Discrete & Continuous Dynamical Systems  B, 2013, 18 (7) : 18451872. doi: 10.3934/dcdsb.2013.18.1845 
[17] 
Yuming Zhang. On continuity equations in spacetime domains. Discrete & Continuous Dynamical Systems  A, 2018, 38 (10) : 48374873. doi: 10.3934/dcds.2018212 
[18] 
Thomas Westerbäck. Parity check systems of nonlinear codes over finite commutative Frobenius rings. Advances in Mathematics of Communications, 2017, 11 (3) : 409427. doi: 10.3934/amc.2017035 
[19] 
DongHo Tsai, ChiaHsing Nien. On spacetime periodic solutions of the onedimensional heat equation. Discrete & Continuous Dynamical Systems  A, 2020, 40 (6) : 39974017. doi: 10.3934/dcds.2020037 
[20] 
Gerard A. Maugin, Martine Rousseau. Prolegomena to studies on dynamic materials and their spacetime homogenization. Discrete & Continuous Dynamical Systems  S, 2013, 6 (6) : 15991608. doi: 10.3934/dcdss.2013.6.1599 
2019 Impact Factor: 0.734
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