Explicit Construction of AG Codes From a Curve in the Tower of Bassa-Beelen-Garcia-Stichtenoth

A method of constructing linear mapping families to achieve the asymptotic GV bound

“…2014 年, 文献 [19] 给出了一种 q 的幂次为 2 以上的奇数情形下的 "函数域塔" 构造, 并证明了对 于所有非素数的素数幂 q 49 (q = 125 除外), 存在渐近参数超过渐近 GV 界的 Shannon 好码渐近序 列. 在该 "函数域塔" 基础上, 文献 [20,21]…”

A Modular Interpretation of BBGS Towers

“…We also would like to point out works of others that are related to the present paper. In the work of Hu and Zhao [31,32], varies bases of certain Riemann-Roch spaces associated to the BBGS tower F are investigated. The interlink between explicit towers and modular curves emerges in Elkies' works [11][12][13], leading to the Elkies' modularity conjecture -all asymptotically optimal recursive towers defined over F q 2 arise from reductions of elliptic, Shimura, or Drinfeld modular curves.…”

“…Good towers that are recursive play important roles in studies of Ihara's quantity, coding theory, and cryptography [1,7,31,32,46,49]. A tower T is called recursive by an absolutely irreducible polynomial f (x, y) ∈ F q (x)[y] (see [42,Sections 3.6 and 7.2]), if…”

Weierstrass Semigroups From a Tower of Function Fields Attaining the Drinfeld-Vladut Bound

“…The curve associated to the second function fields of this tower is called BBGS curve according to [6]. Recently, Hu [12] presented multi-point AG codes overstepping the GV bound from BBGS curves in [6].…”

“…1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 82, 83, 84, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 107, 108,109, 113, 114, 119, 121, 122, 123, 124, 127, 128, 129, 133, 134, 139, 152, 153, 154, 158, 159, 164, 183, 184, 189, 214 …”