MinT - Information on Result #2671657

Information on Result #2671657

Linear OOA(2¹⁴⁴, 64, F₂, 3, 64) (dual of [(64, 3), 48, 65]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁴¹, 63, F₂, 3, 64) (dual of [(63, 3), 48, 65]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁴¹, 63, F₂, 3, 65) (dual of [(63, 3), 48, 66]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4³⁹, 21, F₄, 3, 32) (dual of [(21, 3), 24, 33]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,30P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, 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(2¹⁴⁵, 64, F₂, 3, 64) (dual of [(64, 3), 47, 65]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁴⁶, 64, F₂, 3, 64) (dual of [(64, 3), 46, 65]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁴⁴, 32, F₂, 5, 64) (dual of [(32, 5), 16, 65]-NRT-code)	[i]	OOA Folding
4	Linear OOA(2¹⁴⁴, 32, F₂, 6, 64) (dual of [(32, 6), 48, 65]-NRT-code)	[i]	OOA Folding