MinT - Information on Result #1303092

Information on Result #1303092

Linear OA(9³¹, 238, F₉, 13) (dual of [238, 207, 14]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(9³⁰, 236, F₉, 13) (dual of [236, 206, 14]-code), using
- trace code [i] based on linear OA(81¹⁵, 118, F₈₁, 13) (dual of [118, 103, 14]-code), using
  - extended algebraic-geometric code AG_e(F,104P) [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 118, using
    - sharp bound on the number of rational points on curves with genus 2 [i]
linear OA(9³⁰, 237, F₉, 12) (dual of [237, 207, 13]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 9³⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 21615 586080 098392 378378 716129 [i]
linear OA(9⁰, 1, F₉, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(9³¹, 238, F₉, 2, 13) (dual of [(238, 2), 445, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(9³¹, 238, F₉, 3, 13) (dual of [(238, 3), 683, 14]-NRT-code)	[i]
3	Digital (18, 31, 238)-net over F₉	[i]