MinT - Information on Result #2459409

Information on Result #2459409

Linear OOA(2¹⁸⁸, 104, F₂, 2, 91) (dual of [(104, 2), 20, 92]-NRT-code), using 2 step truncation based on linear OOA(2¹⁹⁰, 105, F₂, 2, 93) (dual of [(105, 2), 20, 94]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁹⁰, 105, F₂, 2, 95) (dual of [(105, 2), 20, 96]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(16¹⁶, 21, F₁₆, 15) (dual of [21, 5, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹⁶, 24, F₁₆, 15) (dual of [24, 8, 16]-code), using
      - extended algebraic-geometric code AG_e(F,8P) [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 OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
      - an explicitly constructive algebraic function field [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(2¹⁸⁸, 52, F₂, 4, 91) (dual of [(52, 4), 20, 92]-NRT-code)	[i]		OOA Folding