MinT - Information on Result #2671956

Information on Result #2671956

Linear OOA(2²²⁷, 137, F₂, 3, 67) (dual of [(137, 3), 184, 68]-NRT-code), using 2² times duplication based on linear OOA(2²²⁵, 137, F₂, 3, 67) (dual of [(137, 3), 186, 68]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(2²²², 136, F₂, 3, 67) (dual of [(136, 3), 186, 68]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(8⁴⁰, 34, F₈, 3, 33) (dual of [(34, 3), 62, 34]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,68P) [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
  2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 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.