MinT - Information on Result #810822

Information on Result #810822

Linear OOA(2²²⁸, 168, F₂, 2, 67) (dual of [(168, 2), 108, 68]-NRT-code), using OOA 2-folding based on linear OA(2²²⁸, 336, F₂, 67) (dual of [336, 108, 68]-code), using

1 times code embedding in larger space [i] 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]

Mode: Constructive and 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.