MinT - Information on Result #2656227

Information on Result #2656227

Linear OOA(2¹⁷³, 71, F₂, 3, 82) (dual of [(71, 3), 40, 83]-NRT-code), using 1 step truncation based on linear OOA(2¹⁷⁴, 72, F₂, 3, 83) (dual of [(72, 3), 42, 84]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁵¹, 24, F₄, 3, 41) (dual of [(24, 3), 21, 42]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁵¹, 26, F₄, 3, 41) (dual of [(26, 3), 27, 42]-NRT-code), using
    - algebraic-geometric NRT-code AG(3;F,36P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]
2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 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(2¹⁷³, 35, F₂, 6, 82) (dual of [(35, 6), 37, 83]-NRT-code)	[i]		OOA Folding