MinT - Information on Result #1301918

Information on Result #1301918

Linear OA(5¹⁴⁵, 166, F₅, 89) (dual of [166, 21, 90]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5¹⁴³, 163, F₅, 89) (dual of [163, 20, 90]-code), using
- 2 times truncation [i] based on linear OA(5¹⁴⁵, 165, F₅, 91) (dual of [165, 20, 92]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(25²³, 33, F₂₅, 22) (dual of [33, 10, 23]-code), using
      - discarding factors / shortening the dual code based on linear OA(25²³, 36, F₂₅, 22) (dual of [36, 13, 23]-code), using
        extended algebraic-geometric code AG_e(F,13P) [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(5¹⁴³, 164, F₅, 87) (dual of [164, 21, 88]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5¹⁴³Â > V_b^sâˆ’1(kâˆ’1)Â = 4693 605823 426990 753706 542632 635749 742313 487218 560046 432361 158564 804493 321387 032122 193153 298388 563965 [i]
linear OA(5¹, 2, F₅, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]

Mode: Linear.

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