MinT - Information on Result #2417969

Information on Result #2417969

Linear OOA(2⁹¹, 50, F₂, 2, 54) (dual of [(50, 2), 9, 55]-NRT-code), using strength reduction based on linear OOA(2⁹¹, 50, F₂, 2, 55) (dual of [(50, 2), 9, 56]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(8⁷, 10, F₈, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,8)), using
  - Denniston code D(1,8) [i]
2. linear OOA(2⁷, 5, F₂, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [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, 51, F₂, 2, 54) (dual of [(51, 2), 9, 55]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2⁹⁵, 52, F₂, 2, 54) (dual of [(52, 2), 9, 55]-NRT-code)	[i]
3	Linear OOA(2⁹⁷, 53, F₂, 2, 54) (dual of [(53, 2), 9, 55]-NRT-code)	[i]
4	Linear OOA(2⁹⁰, 49, F₂, 2, 53) (dual of [(49, 2), 8, 54]-NRT-code)	[i]	Truncation for OOAs
5	Linear OOA(2⁸⁹, 49, F₂, 2, 52) (dual of [(49, 2), 9, 53]-NRT-code)	[i]
6	Linear OOA(2⁸⁷, 48, F₂, 2, 50) (dual of [(48, 2), 9, 51]-NRT-code)	[i]
7	Linear OOA(2⁸⁶, 47, F₂, 2, 49) (dual of [(47, 2), 8, 50]-NRT-code)	[i]
8	Linear OOA(2⁸⁵, 47, F₂, 2, 48) (dual of [(47, 2), 9, 49]-NRT-code)	[i]
9	Linear OOA(2⁹¹, 25, F₂, 4, 54) (dual of [(25, 4), 9, 55]-NRT-code)	[i]	OOA Folding