MinT - Information on Result #1302001

Information on Result #1302001

Linear OA(7⁴³, 186, F₇, 18) (dual of [186, 143, 19]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁴², 184, F₇, 18) (dual of [184, 142, 19]-code), using
- trace code [i] based on linear OA(49²¹, 92, F₄₉, 18) (dual of [92, 71, 19]-code), using
  - extended algebraic-geometric code AG_e(F,73P) [i] based on function field F/F₄₉ with g(F) = 3 and N(F) ≥ 92, using
    - a curve from the manYPoints database [i]
linear OA(7⁴², 185, F₇, 17) (dual of [185, 143, 18]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁴²Â > V_b^sâˆ’1(kâˆ’1)Â = 120849 312361 766561 336729 476435 442497 [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(7⁴³, 179, F₇, 2, 18) (dual of [(179, 2), 315, 19]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound