MinT - Information on Result #2612828

Information on Result #2612828

Linear OOA(2¹⁴², 50, F₂, 3, 97) (dual of [(50, 3), 8, 98]-NRT-code), using strength reduction based on linear OOA(2¹⁴², 50, F₂, 3, 98) (dual of [(50, 3), 8, 99]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁸, 10, F₁₆, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,16)), using
  - discarding factors / shortening the dual code based on linear OA(16⁸, 16, F₁₆, 8) (dual of [16, 8, 9]-code or 16-arc in PG(7,16)), using
    - Reedâ€“Solomon code RS(8,16) [i]
2. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,4P) [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(2¹⁴³, 50, F₂, 3, 97) (dual of [(50, 3), 7, 98]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁴⁰, 49, F₂, 3, 95) (dual of [(49, 3), 7, 96]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2¹³⁹, 49, F₂, 3, 94) (dual of [(49, 3), 8, 95]-NRT-code)	[i]
4	Linear OOA(2¹³⁷, 48, F₂, 3, 92) (dual of [(48, 3), 7, 93]-NRT-code)	[i]
5	Linear OOA(2¹³⁶, 48, F₂, 3, 91) (dual of [(48, 3), 8, 92]-NRT-code)	[i]
6	Linear OOA(2¹³⁴, 47, F₂, 3, 89) (dual of [(47, 3), 7, 90]-NRT-code)	[i]
7	Linear OOA(2¹³³, 47, F₂, 3, 88) (dual of [(47, 3), 8, 89]-NRT-code)	[i]
8	Linear OOA(2¹³², 46, F₂, 3, 87) (dual of [(46, 3), 6, 88]-NRT-code)	[i]
9	Linear OOA(2¹³¹, 46, F₂, 3, 86) (dual of [(46, 3), 7, 87]-NRT-code)	[i]
10	Linear OOA(2¹³⁰, 46, F₂, 3, 85) (dual of [(46, 3), 8, 86]-NRT-code)	[i]
11	Linear OOA(2¹²⁸, 45, F₂, 3, 83) (dual of [(45, 3), 7, 84]-NRT-code)	[i]
12	Linear OOA(2¹⁴², 25, F₂, 6, 97) (dual of [(25, 6), 8, 98]-NRT-code)	[i]	OOA Folding