MinT - Information on Result #2673857

Information on Result #2673857

Linear OOA(2²⁰⁹, 85, F₂, 3, 99) (dual of [(85, 3), 46, 100]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2²⁰⁶, 84, F₂, 3, 99) (dual of [(84, 3), 46, 100]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁶¹, 28, F₄, 3, 49) (dual of [(28, 3), 23, 50]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,34P) [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, 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(2²¹⁰, 85, F₂, 3, 99) (dual of [(85, 3), 45, 100]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2²⁶⁰, 92, F₂, 3, 120) (dual of [(92, 3), 16, 121]-NRT-code)	[i]		Juxtaposition for OOAs