MinT - Information on Result #916045

Information on Result #916045

Linear OOA(3¹⁷⁴, 108, F₃, 2, 92) (dual of [(108, 2), 42, 93]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9³³, 27, F₉, 2, 30) (dual of [(27, 2), 21, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9³³, 28, F₉, 2, 30) (dual of [(28, 2), 23, 31]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,25P) [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, 108, F₃, 2, 91) (dual of [(108, 2), 42, 92]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁷⁴, 108, F₃, 2, 90) (dual of [(108, 2), 42, 91]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3¹⁷⁵, 108, F₃, 2, 92) (dual of [(108, 2), 41, 93]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3¹⁷³, 107, F₃, 2, 91) (dual of [(107, 2), 41, 92]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3¹⁷², 107, F₃, 2, 90) (dual of [(107, 2), 42, 91]-NRT-code)	[i]
6	Linear OOA(3¹⁷¹, 106, F₃, 2, 89) (dual of [(106, 2), 41, 90]-NRT-code)	[i]
7	Linear OOA(3¹⁷⁰, 106, F₃, 2, 88) (dual of [(106, 2), 42, 89]-NRT-code)	[i]
8	Linear OOA(3¹⁶⁹, 105, F₃, 2, 87) (dual of [(105, 2), 41, 88]-NRT-code)	[i]
9	Linear OOA(3¹⁶⁸, 105, F₃, 2, 86) (dual of [(105, 2), 42, 87]-NRT-code)	[i]
10	Linear OOA(3¹⁶⁷, 104, F₃, 2, 85) (dual of [(104, 2), 41, 86]-NRT-code)	[i]
11	Linear OOA(3¹⁷⁴, 54, F₃, 4, 92) (dual of [(54, 4), 42, 93]-NRT-code)	[i]		OOA Folding