MinT - Information on Result #2674297

Information on Result #2674297

Linear OOA(2²⁴², 100, F₂, 3, 111) (dual of [(100, 3), 58, 112]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2²³⁹, 99, F₂, 3, 111) (dual of [(99, 3), 58, 112]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁷⁰, 33, F₄, 3, 55) (dual of [(33, 3), 29, 56]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,43P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, 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(2²⁴³, 100, F₂, 3, 111) (dual of [(100, 3), 57, 112]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁴⁴, 100, F₂, 3, 111) (dual of [(100, 3), 56, 112]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁴², 50, F₂, 6, 111) (dual of [(50, 6), 58, 112]-NRT-code)	[i]	OOA Folding