MinT - Information on Result #1301550

Information on Result #1301550

Linear OA(5⁹⁰, 107, F₅, 55) (dual of [107, 17, 56]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5⁸⁷, 103, F₅, 55) (dual of [103, 16, 56]-code), using
- 1 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(5⁸⁷, 104, F₅, 52) (dual of [104, 17, 53]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5⁸⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 5 265756 402137 300871 972973 069803 811839 862343 433990 108768 615853 [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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