MinT - Information on Result #2461226

Information on Result #2461226

Linear OOA(2²²⁵, 151, F₂, 2, 82) (dual of [(151, 2), 77, 83]-NRT-code), using 1 step truncation based on linear OOA(2²²⁶, 152, F₂, 2, 83) (dual of [(152, 2), 78, 84]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8⁵⁰, 38, F₈, 2, 41) (dual of [(38, 2), 26, 42]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁵⁰, 45, F₈, 2, 41) (dual of [(45, 2), 40, 42]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,48P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²²⁵, 75, F₂, 4, 82) (dual of [(75, 4), 75, 83]-NRT-code)	[i]		OOA Folding