MinT - Information on Result #1301999

Information on Result #1301999

Linear OA(7⁴³, 102, F₇, 21) (dual of [102, 59, 22]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(7⁴², 100, F₇, 21) (dual of [100, 58, 22]-code), using
- trace code [i] based on linear OA(49²¹, 50, F₄₉, 21) (dual of [50, 29, 22]-code or 50-arc in PG(20,49)), using
  - extended Reedâ€“Solomon code RS_e(29,49) [i]
  - the expurgated narrow-sense BCH-code C(I) with length 50Â | 49²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
  - algebraic-geometric code AG(F,14P) with degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using the rational function field F₄₉(x) [i]
  - algebraic-geometric code AG(F, Q+8P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
  - algebraic-geometric code AG(F, Q+5P) with degQ = 3 and degPÂ =Â 5 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
linear OA(7⁴², 101, F₇, 20) (dual of [101, 59, 21]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 7⁴²Â > V_b^sâˆ’1(kâˆ’1)Â = 83874 396930 064244 619761 214306 261601 [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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