MinT - Information on Result #1288690

Information on Result #1288690

Linear OA(25⁸⁵, 88, F₂₅, 80) (dual of [88, 3, 81]-code), using juxtaposition based on

linear OA(25²³, 26, F₂₅, 23) (dual of [26, 3, 24]-code or 26-arc in PG(22,25)), using
- extended Reedâ€“Solomon code RS_e(3,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
- algebraic-geometric code AG(F,1P) with 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+0P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
linear OA(25⁵⁹, 62, F₂₅, 56) (dual of [62, 3, 57]-code), using
- juxtaposition [i] based on
  1. linear OA(25²³, 26, F₂₅, 23) (dual of [26, 3, 24]-code or 26-arc in PG(22,25)) (see above)
  2. linear OA(25³³, 36, F₂₅, 32) (dual of [36, 3, 33]-code), using
    - extended algebraic-geometric code AG_e(F,3P) [i] based on function field F/F₂₅ with g(F) = 1 and N(F) ≥ 36, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

Mode: Linear.

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