MinT - Information on Result #1030580

Information on Result #1030580

Linear OOA(3¹⁵⁰, 60, F₃, 3, 89) (dual of [(60, 3), 30, 90]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9³⁰, 15, F₉, 3, 29) (dual of [(15, 3), 15, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9³⁰, 16, F₉, 3, 29) (dual of [(16, 3), 18, 30]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,18P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, 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(3¹⁵⁰, 60, F₃, 3, 88) (dual of [(60, 3), 30, 89]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3¹⁵¹, 60, F₃, 3, 89) (dual of [(60, 3), 29, 90]-NRT-code)	[i]		OOA Duplication
3	Linear OOA(3¹⁴⁹, 59, F₃, 3, 88) (dual of [(59, 3), 28, 89]-NRT-code)	[i]		Truncation for OOAs
4	Linear OOA(3¹⁴⁸, 59, F₃, 3, 87) (dual of [(59, 3), 29, 88]-NRT-code)	[i]
5	Linear OOA(3¹⁴⁷, 59, F₃, 3, 86) (dual of [(59, 3), 30, 87]-NRT-code)	[i]
6	Linear OOA(3¹⁴⁶, 58, F₃, 3, 85) (dual of [(58, 3), 28, 86]-NRT-code)	[i]
7	Linear OOA(3¹⁴⁵, 58, F₃, 3, 84) (dual of [(58, 3), 29, 85]-NRT-code)	[i]
8	Linear OOA(3¹⁴⁴, 58, F₃, 3, 83) (dual of [(58, 3), 30, 84]-NRT-code)	[i]
9	Linear OOA(3¹⁴², 57, F₃, 3, 81) (dual of [(57, 3), 29, 82]-NRT-code)	[i]
10	Linear OOA(3¹⁴¹, 57, F₃, 3, 80) (dual of [(57, 3), 30, 81]-NRT-code)	[i]