MinT - Information on Result #1301544

Information on Result #1301544

Linear OA(5⁸⁹, 106, F₅, 54) (dual of [106, 17, 55]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5⁸⁶, 102, F₅, 54) (dual of [102, 16, 55]-code), using
- 2 times truncation [i] based on linear OA(5⁸⁸, 104, F₅, 56) (dual of [104, 16, 57]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(25¹⁸, 26, F₂₅, 18) (dual of [26, 8, 19]-code or 26-arc in PG(17,25)), using
      - extended Reedâ€“Solomon code RS_e(8,25) [i]
      - algebraic-geometric code AG(F, Q+2P) 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, Q+1P) with degQ = 4 and 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(5⁸⁶, 103, F₅, 51) (dual of [103, 17, 52]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5⁸⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 647899 756644 784962 839347 307860 184157 086500 349640 034652 569481 [i]
linear OA(5², 3, F₅, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,5)), using
- dual of repetition code with length 3 [i]

Mode: Linear.

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