MinT - Information on Result #1301806

Information on Result #1301806

Linear OA(5¹²⁸, 150, F₅, 77) (dual of [150, 22, 78]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5¹²⁴, 144, F₅, 77) (dual of [144, 20, 78]-code), using
- concatenation of two codes [i] based on
  1. linear OA(25²⁶, 36, F₂₅, 25) (dual of [36, 10, 26]-code), using
    - extended algebraic-geometric code AG_e(F,10P) [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(5¹²⁴, 146, F₅, 74) (dual of [146, 22, 75]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5¹²⁴Â > V_b^sâˆ’1(kâˆ’1)Â = 348 678603 423894 744352 431853 685731 172611 686740 482152 377025 253193 496490 135923 032690 582725 [i]
linear OA(5², 4, F₅, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,5)) (see above)

Mode: Linear.

None.

None.