Constructions of Dense Lattices over Number Fields
نویسندگان
چکیده
منابع مشابه
Short Bases of Lattices over Number Fields
Lattices over number elds arise from a variety of sources in algorithmic algebra and more recently cryptography. Similar to the classical case of Z-lattices, the choice of a nice, short (pseudo)-basis is important in many applications. In this article, we provide the rst algorithm that computes such a short (pseudo)-basis. We utilize the LLL algorithm for Z-lattices together with the Bosma-Pohs...
متن کاملConstructions of Orthonormal Lattices and Quaternion Division Algebras for Totally Real Number Fields
We describe some constructions of orthonormal lattices in totally real subfields of cyclotomic fields, obtained by endowing their ring of integers with a trace form. We also describe constructions of quaternion division algebras over such fields. Orthonormal lattices and quaternion division algebras over totally real fields find use in wireless networks in ultra wideband communication, and we d...
متن کاملConstructions of Codes from Number Fields
We define number-theoretic error-correcting codes based on algebraic number fields, thereby providing a generalization of Chinese Remainder Codes akin to the generalization of ReedSolomon codes to Algebraic-geometric codes. Our construction is very similar to (and in fact less general than) the one given by Lenstra [9], but the parallel with the function field case is more apparent, since we on...
متن کاملConstructions of Subsystem Codes over Finite Fields
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This paper introduces numerous constructions of subsystem codes. It is shown how one can derive subsystem codes from classical cyclic codes. Methods to trade the dim...
متن کاملLattices from elliptic curves over finite fields
In their well known book [6] Tsfasman and Vladut introduced a construction of a family of function field lattices from algebraic curves over finite fields, which have asymptotically good packing density in high dimensions. In this paper we study geometric properties of lattices from this construction applied to elliptic curves. In particular, we determine the generating sets, conditions for wel...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: TEMA (São Carlos)
سال: 2020
ISSN: 2179-8451,1677-1966
DOI: 10.5540/tema.2020.021.01.57