MinT - Information on Result #1301821

Information on Result #1301821

Linear OA(5¹²⁹, 148, F₅, 80) (dual of [148, 19, 81]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5¹²⁶, 144, F₅, 80) (dual of [144, 18, 81]-code), using
- concatenation of two codes [i] based on
  1. linear OA(25²⁷, 36, F₂₅, 26) (dual of [36, 9, 27]-code), using
    - extended algebraic-geometric code AG_e(F,9P) [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]
  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(5¹²⁶, 145, F₅, 77) (dual of [145, 19, 78]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5¹²⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 9315 951505 961468 595439 277491 213702 918540 049961 434896 762033 290070 741979 600799 633379 962305 [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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None.