Automatic and polynomial-time algebraic structures by Bazhenov, Nikolay, Harrison-Trainor, Matthew, Kalimullin, Iskander, Melnikov, Alexander, Ng, Keng Meng

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On the algebraic structure of quasi-cyclic codes III : generator theory by Ling, San, Sole, Patrick

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On the algebraic structure of quasi-cyclic codes II : chain rings by Ling, San, Sole, Patrick

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On the algebraic structure of quasi-cyclic codes I : finite fields by Ling, San, Sole, Patrick

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A structure of punctual dimension two by Melnikov, Alexander, Ng, Keng Meng

“…We prove that there exists a countable rigid algebraic structure which has exactly two punctual presentations, up to punctual isomorphism.…”
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Emergent commensurability from Hilbert space truncation in fractional quantum Hall fluids by Yang, Bo

“…We also discuss the implications of certain missing states proposed from other phenomenological approaches, and suggest that the physics of the FQH effect could fundamentally arise from the algebraic structure of the Hilbert space in a single Landau level.…”
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Projectively enriched symmetry and topology in acoustic crystals by Xue, Haoran, Wang, Zihao, Huang, Yue-Xin, Cheng, Zheyu, Yu, Letian, Foo, Y. X., Zhao, Y. X., Yang, Shengyuan A., Zhang, Baile

“…Here, we show that the algebraic structure of crystal symmetries can be projectively enriched due to the gauge symmetry, which subsequently gives rise to new topological physics never witnessed under ordinary symmetries. …”
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Spinful topological phases in acoustic crystals with projective PT symmetry by Meng, Yan, Lin, Shuxin, Shi, Bin-Jie, Wei, Bin, Yang, Linyun, Yan, Bei, Zhu, Zhenxiao, Xi, Xiang, Wang, Yin, Ge, Yong, Yuan, Shou-Qi, Chen, Jingming, Liu, Gui-Geng, Sun, Hong-Xiang, Chen, Hongsheng, Yang, Yihao, Gao, Zhen

“…However, only recently has it been realized theoretically that in the presence of gauge symmetry, the algebraic structure of symmetries can be projectively represented, which possibly enables the switch between spinless and spinful topological phases. …”
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Generalized negacyclic codes over finite fields by Jitman, Somphong, Ling, San, Tharnnukhroh, Jareena

“…Linear codes with additional algebraic structures such as cyclic codes, negacyclic codes and abelian codes have become of interest due to their nice algebraic structures, wide applications and links with other mathematical objects. …”
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A new canonical affine bracket formulation of Hamiltonian classical field theories of first order by Gay-Balmaz, François, Marrero, Juan C., Alba, Nicolás Martínez

“…This Lie algebra structure is shown to have a representation on the affine space of Hamiltonian sections, which yields an affine analogue to the Jacobi identity for our bracket. …”
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Algebraic fast-decodable relay codes for distributed communications by Hollanti, Camilla, Markin, Nadya

“…The constructions are based on different types of algebraic structures, e.g. quaternion division algebras. …”
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Skew cyclic codes over F4R by Benbelkacem, Nasreddin, Ezerman, Martianus Frederic, Abualrub, Taher, Aydin, Nuh, Batoul, Aicha

“…Results on the algebraic structures lead us to characterize 4R-skew cyclic codes. …”
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Type-II polyadic constacyclic codes over finite fields by Jitman, Somphong, Ling, San, Tharnnukhroh, Jareena

“…Polyadic constacyclic codes over finite fields have been of interest due to their nice algebraic structures, good parameters, and wide applications. …”
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Self-dual and complementary dual abelian codes over Galois rings by Jitman, Somphong, Ling, San

“…Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications. In this paper, abelian codes over Galois rings are studied in terms of the ideals in the group ring GR(pr,s)[G], where G is a finite abelian group and GR(pr,s) is a Galois ring. …”
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Codes over matrix rings for space-time coded modulations by Oggier, Frederique, Sole, Patrick, Belfiore, Jean-Claude

“…When the inner code has a cyclic algebra structure over a number field, as for perfect space-time codes, an outer code can be designed via coset coding, more precisely, by taking the quotient of the algebra by a two-sided ideal which leads to matrices over finite alphabets for the outer code. …”
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