MinT - Information on Result #1302011

Information on Result #1302011

Linear OA(7⁴⁵, 130, F₇, 21) (dual of [130, 85, 22]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁴⁴, 128, F₇, 21) (dual of [128, 84, 22]-code), using
- trace code [i] based on linear OA(49²², 64, F₄₉, 21) (dual of [64, 42, 22]-code), using
  - extended algebraic-geometric code AG_e(F,42P) [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(7⁴⁴, 129, F₇, 20) (dual of [129, 85, 21]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁴⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 13 774534 631245 692102 017257 383386 606593 [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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