MinT - Information on Result #1297581

Information on Result #1297581

Linear OA(2²³⁷, 350, F₂, 66) (dual of [350, 113, 67]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(2²²⁷, 335, F₂, 67) (dual of [335, 108, 68]-code), using
- concatenation of two codes [i] based on
  1. linear OA(16⁴⁰, 67, F₁₆, 33) (dual of [67, 27, 34]-code), using
    - constructionÂ X applied to AG(F,30P) âŠ‚ AG(F,32P) [i] based on
      1. linear OA(16³⁹, 64, F₁₆, 33) (dual of [64, 25, 34]-code), using algebraic-geometric code AG(F,30P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]
      2. linear OA(16³⁷, 64, F₁₆, 31) (dual of [64, 27, 32]-code), using algebraic-geometric code AG(F,32P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
      3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(2²²⁷, 340, F₂, 62) (dual of [340, 113, 63]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2²²⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 175 918841 839473 351634 568765 383862 502088 054225 267157 842891 554412 674080 [i]
linear OA(2⁵, 10, F₂, 3) (dual of [10, 5, 4]-code or 10-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(2⁵, 16, F₂, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
  - Reedâ€“Muller code RM(1,4) [i]
  - caps in base bÂ =Â 2 [i]

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.