MinT - Information on Result #1132661

Information on Result #1132661

Linear OOA(2⁵⁷, 13, F₂, 6, 29) (dual of [(13, 6), 21, 30]-NRT-code), using OOA 2-folding based on linear OOA(2⁵⁷, 26, F₂, 3, 29) (dual of [(26, 3), 21, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁵⁷, 27, F₂, 3, 29) (dual of [(27, 3), 24, 30]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4¹⁵, 9, F₄, 3, 14) (dual of [(9, 3), 12, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,12P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
      - the Hermitian function field over F₄ [i]
  2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 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.