MinT - Information on Result #916029

Information on Result #916029

Linear OOA(3¹⁷⁴, 112, F₃, 2, 86) (dual of [(112, 2), 50, 87]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9³¹, 28, F₉, 2, 28) (dual of [(28, 2), 25, 29]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,27P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
  - the Hermitian function field over F₉ [i]
linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reedâ€“Solomon code RS_e(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [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(3¹⁷⁴, 112, F₃, 2, 85) (dual of [(112, 2), 50, 86]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁷⁴, 112, F₃, 2, 84) (dual of [(112, 2), 50, 85]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3¹⁷⁶, 113, F₃, 2, 86) (dual of [(113, 2), 50, 87]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(3¹⁷⁵, 112, F₃, 2, 86) (dual of [(112, 2), 49, 87]-NRT-code)	[i]		OOA Duplication
5	Linear OOA(3¹⁷³, 111, F₃, 2, 85) (dual of [(111, 2), 49, 86]-NRT-code)	[i]		Truncation for OOAs
6	Linear OOA(3¹⁷², 111, F₃, 2, 84) (dual of [(111, 2), 50, 85]-NRT-code)	[i]
7	Linear OOA(3¹⁷¹, 110, F₃, 2, 83) (dual of [(110, 2), 49, 84]-NRT-code)	[i]
8	Linear OOA(3¹⁷⁰, 110, F₃, 2, 82) (dual of [(110, 2), 50, 83]-NRT-code)	[i]
9	Linear OOA(3¹⁶⁹, 109, F₃, 2, 81) (dual of [(109, 2), 49, 82]-NRT-code)	[i]
10	Linear OOA(3¹⁶⁸, 109, F₃, 2, 80) (dual of [(109, 2), 50, 81]-NRT-code)	[i]
11	Linear OOA(3¹⁷⁴, 56, F₃, 4, 86) (dual of [(56, 4), 50, 87]-NRT-code)	[i]		OOA Folding