MinT - Information on Result #2670115

Information on Result #2670115

Linear OOA(2¹¹⁸, 56, F₂, 3, 49) (dual of [(56, 3), 50, 50]-NRT-code), using 2¹ times duplication based on linear OOA(2¹¹⁷, 56, F₂, 3, 49) (dual of [(56, 3), 51, 50]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8²⁵, 14, F₈, 3, 24) (dual of [(14, 3), 17, 25]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,17P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
    - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [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.