MinT - Information on Result #1301527

Information on Result #1301527

Linear OA(5⁸³, 104, F₅, 48) (dual of [104, 21, 49]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5⁸², 102, F₅, 48) (dual of [102, 20, 49]-code), using
- 2 times truncation [i] based on linear OA(5⁸⁴, 104, F₅, 50) (dual of [104, 20, 51]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(25¹⁶, 26, F₂₅, 16) (dual of [26, 10, 17]-code or 26-arc in PG(15,25)), using
      - extended Reedâ€“Solomon code RS_e(10,25) [i]
      - algebraic-geometric code AG(F, Q+3P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
      - algebraic-geometric code AG(F,3P) with degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
    2. linear OA(5², 4, F₅, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,5)), using
      - discarding factors / shortening the dual code based on linear OA(5², 5, F₅, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,5)), using
        Reedâ€“Solomon code RS(3,5) [i]
linear OA(5⁸², 103, F₅, 47) (dual of [103, 21, 48]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5⁸²Â > V_b^sâˆ’1(kâˆ’1)Â = 1520 803367 087680 585731 665590 184069 477293 535523 265015 496585 [i]
linear OA(5⁰, 1, F₅, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 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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