MinT - Information on Result #1030602

Information on Result #1030602

Linear OOA(3¹⁸⁴, 72, F₃, 3, 110) (dual of [(72, 3), 32, 111]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9³⁸, 18, F₉, 3, 36) (dual of [(18, 3), 16, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9³⁸, 20, F₉, 3, 36) (dual of [(20, 3), 22, 37]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,23P) [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
    - a function field by GarcÃa and Quoos [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(3¹⁸⁴, 72, F₃, 3, 109) (dual of [(72, 3), 32, 110]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁸⁴, 72, F₃, 3, 108) (dual of [(72, 3), 32, 109]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3¹⁸⁵, 72, F₃, 3, 110) (dual of [(72, 3), 31, 111]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(3¹⁸³, 71, F₃, 3, 109) (dual of [(71, 3), 30, 110]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(3¹⁸², 71, F₃, 3, 108) (dual of [(71, 3), 31, 109]-NRT-code)	[i]
6	Linear OOA(3¹⁸¹, 71, F₃, 3, 107) (dual of [(71, 3), 32, 108]-NRT-code)	[i]
7	Linear OOA(3¹⁸⁰, 70, F₃, 3, 106) (dual of [(70, 3), 30, 107]-NRT-code)	[i]
8	Linear OOA(3¹⁷⁹, 70, F₃, 3, 105) (dual of [(70, 3), 31, 106]-NRT-code)	[i]
9	Linear OOA(3¹⁷⁸, 70, F₃, 3, 104) (dual of [(70, 3), 32, 105]-NRT-code)	[i]
10	Linear OOA(3¹⁷⁶, 69, F₃, 3, 102) (dual of [(69, 3), 31, 103]-NRT-code)	[i]