MinT - Information on Result #1301890

Information on Result #1301890

Linear OA(5¹⁴⁰, 162, F₅, 85) (dual of [162, 22, 86]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(5¹³⁹, 160, F₅, 85) (dual of [160, 21, 86]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(5¹³⁸, 158, F₅, 85) (dual of [158, 20, 86]-code), using
    - 2 times truncation [i] based on linear OA(5¹⁴⁰, 160, F₅, 87) (dual of [160, 20, 88]-code), using
      - concatenation of two codes [i] based on
        linear OA(25²², 32, F₂₅, 21) (dual of [32, 10, 22]-code), using
        discarding factors / shortening the dual code based on linear OA(25²², 36, F₂₅, 21) (dual of [36, 14, 22]-code), using
        extended algebraic-geometric code AG_e(F,14P) [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]
        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]
  2. linear OA(5¹³⁸, 159, F₅, 84) (dual of [159, 21, 85]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5¹³⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 2 427795 119481 531951 363406 710166 216200 530843 770075 093405 237919 683991 470590 336755 218795 375174 067625 [i]
  3. linear OA(5⁰, 1, F₅, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]
linear OA(5¹³⁹, 161, F₅, 84) (dual of [161, 22, 85]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5¹³⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 10 456319 684040 271487 930641 301451 644602 869977 587958 017158 545822 030977 984934 411620 035432 929441 295745 [i]
linear OA(5⁰, 1, F₅, 0) (dual of [1, 1, 1]-code) (see above)

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.