MinT - Information on Result #1302044

Information on Result #1302044

Linear OA(7⁵¹, 158, F₇, 23) (dual of [158, 107, 24]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁵⁰, 156, F₇, 23) (dual of [156, 106, 24]-code), using
- trace code [i] based on linear OA(49²⁵, 78, F₄₉, 23) (dual of [78, 53, 24]-code), using
  - extended algebraic-geometric code AG_e(F,54P) [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(7⁵⁰, 157, F₇, 22) (dual of [157, 107, 23]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁵⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 1 223749 981641 007031 348664 572779 027252 437409 [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.

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