MinT - Information on Result #661549

Information on Result #661549

Linear OA(5¹²³, 145, F₅, 71) (dual of [145, 22, 72]-code), using concatenation of two codes based on

linear OA(25¹⁸, 29, F₂₅, 17) (dual of [29, 11, 18]-code), using
- constructionÂ X applied to AG(F,4P) âŠ‚ AG(F,5P) [i] based on
  1. linear OA(25¹⁷, 26, F₂₅, 17) (dual of [26, 9, 18]-code or 26-arc in PG(16,25)), using algebraic-geometric code AG(F,4P) 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]
  2. linear OA(25¹⁵, 26, F₂₅, 15) (dual of [26, 11, 16]-code or 26-arc in PG(14,25)), using algebraic-geometric code AG(F,5P) with degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
  3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(5³, 5, F₅, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,5) or 5-cap in PG(2,5)), using
- Reedâ€“Solomon code RS(2,5) [i]

Mode: Constructive and linear.

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