MinT - Information on Result #1301924

Information on Result #1301924

Linear OA(5¹⁵⁰, 167, F₅, 96) (dual of [167, 17, 97]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5¹⁴⁶, 162, F₅, 96) (dual of [162, 16, 97]-code), using
- 3 times truncation [i] based on linear OA(5¹⁴⁹, 165, F₅, 99) (dual of [165, 16, 100]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(25²⁵, 33, F₂₅, 24) (dual of [33, 8, 25]-code), using
      - discarding factors / shortening the dual code based on linear OA(25²⁵, 36, F₂₅, 24) (dual of [36, 11, 25]-code), using
        extended algebraic-geometric code AG_e(F,11P) [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(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]
linear OA(5¹⁴⁶, 163, F₅, 92) (dual of [163, 17, 93]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5¹⁴⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 953605 413048 121628 116578 667448 449086 289117 917091 099797 972516 139189 110036 939188 625028 859981 626191 344025 [i]
linear OA(5³, 4, F₅, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,5) or 4-cap in PG(2,5)), using
- dual of repetition code with length 4 [i]

Mode: Linear.

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