MinT - Information on Result #1302058

Information on Result #1302058

Linear OA(7⁵³, 158, F₇, 24) (dual of [158, 105, 25]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁵², 156, F₇, 24) (dual of [156, 104, 25]-code), using
- trace code [i] based on linear OA(49²⁶, 78, F₄₉, 24) (dual of [78, 52, 25]-code), using
  - extended algebraic-geometric code AG_e(F,53P) [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(7⁵², 157, F₇, 23) (dual of [157, 105, 24]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁵²Â > V_b^sâˆ’1(kâˆ’1)Â = 45 122129 417398 590386 503011 801365 319219 208609 [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.

None.