MinT - Information on Result #2610894

Information on Result #2610894

Linear OOA(2⁹⁰, 42, F₂, 3, 42) (dual of [(42, 3), 36, 43]-NRT-code), using strength reduction based on linear OOA(2⁹⁰, 42, F₂, 3, 43) (dual of [(42, 3), 36, 44]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4²⁴, 14, F₄, 3, 21) (dual of [(14, 3), 18, 22]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,20P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, 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(2⁹³, 43, F₂, 3, 42) (dual of [(43, 3), 36, 43]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2⁹¹, 42, F₂, 3, 42) (dual of [(42, 3), 35, 43]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2⁹⁰, 21, F₂, 5, 42) (dual of [(21, 5), 15, 43]-NRT-code)	[i]	OOA Folding
4	Linear OOA(2⁹⁰, 21, F₂, 6, 42) (dual of [(21, 6), 36, 43]-NRT-code)	[i]	OOA Folding