MinT - Information on Result #916078

Information on Result #916078

Linear OOA(3¹⁷⁴, 100, F₃, 2, 104) (dual of [(100, 2), 26, 105]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9³⁷, 25, F₉, 2, 34) (dual of [(25, 2), 13, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9³⁷, 28, F₉, 2, 34) (dual of [(28, 2), 19, 35]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,21P) [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, 100, F₃, 2, 103) (dual of [(100, 2), 26, 104]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁷⁴, 100, F₃, 2, 102) (dual of [(100, 2), 26, 103]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3¹⁷⁵, 100, F₃, 2, 104) (dual of [(100, 2), 25, 105]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3¹⁷³, 99, F₃, 2, 103) (dual of [(99, 2), 25, 104]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3¹⁷², 99, F₃, 2, 102) (dual of [(99, 2), 26, 103]-NRT-code)	[i]
6	Linear OOA(3¹⁷¹, 98, F₃, 2, 101) (dual of [(98, 2), 25, 102]-NRT-code)	[i]
7	Linear OOA(3¹⁷⁰, 98, F₃, 2, 100) (dual of [(98, 2), 26, 101]-NRT-code)	[i]
8	Linear OOA(3¹⁶⁹, 97, F₃, 2, 99) (dual of [(97, 2), 25, 100]-NRT-code)	[i]
9	Linear OOA(3¹⁶⁸, 97, F₃, 2, 98) (dual of [(97, 2), 26, 99]-NRT-code)	[i]
10	Linear OOA(3¹⁶⁷, 96, F₃, 2, 97) (dual of [(96, 2), 25, 98]-NRT-code)	[i]
11	Linear OOA(3¹⁷⁴, 50, F₃, 4, 104) (dual of [(50, 4), 26, 105]-NRT-code)	[i]		OOA Folding