MinT - Information on Result #912902

Information on Result #912902

Linear OOA(3²⁴³, 126, F₃, 2, 170) (dual of [(126, 2), 9, 171]-NRT-code), using concatenation of two NRT-codes based on

linear OA(27¹⁸, 21, F₂₇, 18) (dual of [21, 3, 19]-code or 21-arc in PG(17,27)), using
- discarding factors / shortening the dual code based on linear OA(27¹⁸, 27, F₂₇, 18) (dual of [27, 9, 19]-code or 27-arc in PG(17,27)), using
  - Reedâ€“Solomon code RS(9,27) [i]
linear OOA(3⁹, 6, F₃, 2, 8) (dual of [(6, 2), 3, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁹, 7, F₃, 2, 8) (dual of [(7, 2), 5, 9]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, 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		This result only	Method
1	Linear OOA(3²⁴³, 126, F₃, 2, 169) (dual of [(126, 2), 9, 170]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²⁴³, 126, F₃, 2, 168) (dual of [(126, 2), 9, 169]-NRT-code)	[i]
3	Linear OOA(3²⁴³, 126, F₃, 2, 167) (dual of [(126, 2), 9, 168]-NRT-code)	[i]
4	Linear OOA(3²⁴², 125, F₃, 2, 169) (dual of [(125, 2), 8, 170]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3²⁴¹, 125, F₃, 2, 168) (dual of [(125, 2), 9, 169]-NRT-code)	[i]
6	Linear OOA(3²³⁸, 123, F₃, 2, 165) (dual of [(123, 2), 8, 166]-NRT-code)	[i]
7	Linear OOA(3²³⁷, 123, F₃, 2, 164) (dual of [(123, 2), 9, 165]-NRT-code)	[i]
8	Linear OOA(3²³⁶, 122, F₃, 2, 163) (dual of [(122, 2), 8, 164]-NRT-code)	[i]
9	Linear OOA(3²³⁵, 122, F₃, 2, 162) (dual of [(122, 2), 9, 163]-NRT-code)	[i]
10	Linear OOA(3²³⁴, 121, F₃, 2, 161) (dual of [(121, 2), 8, 162]-NRT-code)	[i]
11	Linear OOA(3²³³, 121, F₃, 2, 160) (dual of [(121, 2), 9, 161]-NRT-code)	[i]
12	Linear OOA(3²³⁰, 119, F₃, 2, 157) (dual of [(119, 2), 8, 158]-NRT-code)	[i]