MinT - Information on Result #2656406

Information on Result #2656406

Linear OOA(2¹⁶⁸, 74, F₂, 3, 74) (dual of [(74, 3), 54, 75]-NRT-code), using 1 step truncation based on linear OOA(2¹⁶⁹, 75, F₂, 3, 75) (dual of [(75, 3), 56, 76]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁴⁷, 25, F₄, 3, 37) (dual of [(25, 3), 28, 38]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁴⁷, 26, F₄, 3, 37) (dual of [(26, 3), 31, 38]-NRT-code), using
    - algebraic-geometric NRT-code AG(3;F,40P) [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(2¹⁶⁸, 37, F₂, 6, 74) (dual of [(37, 6), 54, 75]-NRT-code)	[i]		OOA Folding