MinT - Information on Result #1301983

Information on Result #1301983

Linear OA(7³⁷, 158, F₇, 16) (dual of [158, 121, 17]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7³⁶, 156, F₇, 16) (dual of [156, 120, 17]-code), using
- trace code [i] based on linear OA(49¹⁸, 78, F₄₉, 16) (dual of [78, 60, 17]-code), using
  - extended algebraic-geometric code AG_e(F,61P) [i] based on function field F/F₄₉ with g(F) = 2 and N(F) ≥ 78, using
    - sharp bound on the number of rational points on curves with genus 2 [i]
linear OA(7³⁶, 157, F₇, 15) (dual of [157, 121, 16]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7³⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 2 532851 123521 743095 837168 361889 [i]
linear OA(7⁰, 1, F₇, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 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		This result only	Method
1	Linear OOA(7³⁷, 143, F₇, 2, 16) (dual of [(143, 2), 249, 17]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound