MinT - Information on Result #2458704

Information on Result #2458704

Linear OOA(2¹²⁵, 104, F₂, 2, 40) (dual of [(104, 2), 83, 41]-NRT-code), using 1 step truncation based on linear OOA(2¹²⁶, 105, F₂, 2, 41) (dual of [(105, 2), 84, 42]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16²¹, 21, F₁₆, 2, 20) (dual of [(21, 2), 21, 21]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16²¹, 24, F₁₆, 2, 20) (dual of [(24, 2), 27, 21]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,27P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹²⁵, 52, F₂, 4, 40) (dual of [(52, 4), 83, 41]-NRT-code)	[i]		OOA Folding