MinT - Information on Result #2461464

Information on Result #2461464

Linear OOA(2²¹⁵, 209, F₂, 2, 58) (dual of [(209, 2), 203, 59]-NRT-code), using 1 step truncation based on linear OOA(2²¹⁶, 210, F₂, 2, 59) (dual of [(210, 2), 204, 60]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16³³, 42, F₁₆, 2, 29) (dual of [(42, 2), 51, 30]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16³³, 45, F₁₆, 2, 29) (dual of [(45, 2), 57, 30]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,60P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [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(2²¹⁵, 104, F₂, 4, 58) (dual of [(104, 4), 201, 59]-NRT-code)	[i]		OOA Folding