Nettet15. mai 2024 · In this paper, we presented a family of linear codes with defining set \(D_Q^a\), where \(a\in F_q\) and Q(x) is any quadratic form, and determined their complete weight enumerators. Our results are extensions of earlier related works and … Nettetbut it can be viewed as a quadratic form over Q, Z p for p =2 , Q 2, R or C since −1 2 lies in each of those rings. In fact it can be viewed as a quadratic form over Z/nZ for any odd n,as−2 is invertible mod n whenever n is odd. The subject of quadratic forms is vast and central to many parts of mathematics, such as linear
Is there a systematic way of finding the matrix of a quadratic form ...
NettetUniversity of Michigan. Jun 2015 - Jul 20152 months. Ann Arbor, Michigan, United States. Studied Graph Theory and the relationships between distinct objects on campus. Described vertices ... Nettet1. mar. 2024 · Converting from quadratic form to standard form is quite common, so you can also check out this helpful video for another example. Return to the Table of Contents. Convert from Factored Form to Standard Form. To convert an equation from factored form into standard form simply involves multiplying the factors. family homeless shelters in mesa az
Vectorial bent functions and Linear Codes from Quadratic Forms
NettetQuadratic forms in general encode the so-called "quadric surfaces" such as ellipses, hyperbolic paraboloids, and so on. The principal axis theorem, also known as the spectral theorem, is one of the most important theorems in linear algebra! It is what allows us to "transform" the quadratic forms your professor mentioned. Nettet8. feb. 2015 · 2 Answers Sorted by: 2 There's another approach: the Gauss decomposition consists to write the quadratic form on sum of squares. We have Q ( x, y) = 3 x 2 − ( 5 + c) x y + 2 c y 2 = 3 ( x − 5 + c 6 y) 2 + ( 2 c − ( 5 + c) 2 12) y 2 so the discussion is on the sign of α ( c) = 2 c − ( 5 + c) 2 12 if α ( c) > 0 then Q is positive definite Nettet7. des. 2024 · [Submitted on 7 Dec 2024] Generalized Hamming Weights of Linear Codes from Quadratic Forms over Finite Fields of Even Characteristic Chao Liu, Dabin Zheng, Xiaoqiang Wang The generalized Hamming weight of linear codes is a natural generalization of the minimum Hamming distance. hl sebastian telfs