MinT - Information on Result #2672465

Information on Result #2672465

Linear OOA(2¹⁷⁸, 82, F₂, 3, 74) (dual of [(82, 3), 68, 75]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁷⁵, 81, F₂, 3, 74) (dual of [(81, 3), 68, 75]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁷⁵, 81, F₂, 3, 75) (dual of [(81, 3), 68, 76]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4⁴⁷, 27, F₄, 3, 37) (dual of [(27, 3), 34, 38]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,43P) [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		Method
1	Linear OOA(2¹⁷⁹, 82, F₂, 3, 74) (dual of [(82, 3), 67, 75]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁸⁰, 82, F₂, 3, 74) (dual of [(82, 3), 66, 75]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁷⁸, 41, F₂, 5, 74) (dual of [(41, 5), 27, 75]-NRT-code)	[i]	OOA Folding
4	Linear OOA(2¹⁷⁸, 41, F₂, 6, 74) (dual of [(41, 6), 68, 75]-NRT-code)	[i]	OOA Folding