MinT - Information on Result #916077

Information on Result #916077

Linear OOA(3¹⁷⁸, 104, F₃, 2, 104) (dual of [(104, 2), 30, 105]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9³⁷, 26, F₉, 2, 34) (dual of [(26, 2), 15, 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(3¹⁷⁸, 104, F₃, 2, 103) (dual of [(104, 2), 30, 104]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁷⁸, 104, F₃, 2, 102) (dual of [(104, 2), 30, 103]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3¹⁷⁹, 104, F₃, 2, 104) (dual of [(104, 2), 29, 105]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3¹⁷⁷, 103, F₃, 2, 103) (dual of [(103, 2), 29, 104]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3¹⁷⁶, 103, F₃, 2, 102) (dual of [(103, 2), 30, 103]-NRT-code)	[i]
6	Linear OOA(3¹⁷⁵, 102, F₃, 2, 101) (dual of [(102, 2), 29, 102]-NRT-code)	[i]
7	Linear OOA(3¹⁷⁴, 102, F₃, 2, 100) (dual of [(102, 2), 30, 101]-NRT-code)	[i]
8	Linear OOA(3¹⁷³, 101, F₃, 2, 99) (dual of [(101, 2), 29, 100]-NRT-code)	[i]
9	Linear OOA(3¹⁷², 101, F₃, 2, 98) (dual of [(101, 2), 30, 99]-NRT-code)	[i]
10	Linear OOA(3¹⁷¹, 100, F₃, 2, 97) (dual of [(100, 2), 29, 98]-NRT-code)	[i]
11	Linear OOA(3¹⁷⁸, 52, F₃, 4, 104) (dual of [(52, 4), 30, 105]-NRT-code)	[i]		OOA Folding