MinT - Information on Result #1302042

Information on Result #1302042

Linear OA(7⁵¹, 130, F₇, 24) (dual of [130, 79, 25]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁵⁰, 128, F₇, 24) (dual of [128, 78, 25]-code), using
- trace code [i] based on linear OA(49²⁵, 64, F₄₉, 24) (dual of [64, 39, 25]-code), using
  - extended algebraic-geometric code AG_e(F,39P) [i] based on function field F/F₄₉ with g(F) = 1 and N(F) ≥ 64, using
    - sharp bound on the number of rational points on curves with genus 1 [i]
linear OA(7⁵⁰, 129, F₇, 23) (dual of [129, 79, 24]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁵⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 407890 760291 712425 393321 578540 839774 907393 [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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