MinT - Information on Result #916188

Information on Result #916188

Linear OOA(3²³⁰, 128, F₃, 2, 140) (dual of [(128, 2), 26, 141]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(9⁵¹, 32, F₉, 2, 46) (dual of [(32, 2), 13, 47]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,17P) [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, 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(3²³⁰, 128, F₃, 2, 139) (dual of [(128, 2), 26, 140]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(3²³⁰, 128, F₃, 2, 138) (dual of [(128, 2), 26, 139]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(3²³², 129, F₃, 2, 140) (dual of [(129, 2), 26, 141]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
4	Linear OOA(3²³¹, 128, F₃, 2, 140) (dual of [(128, 2), 25, 141]-NRT-code)	[i]		OOA Duplication
5	Linear OOA(3²²⁹, 127, F₃, 2, 139) (dual of [(127, 2), 25, 140]-NRT-code)	[i]		Truncation for OOAs
6	Linear OOA(3²²⁸, 127, F₃, 2, 138) (dual of [(127, 2), 26, 139]-NRT-code)	[i]
7	Linear OOA(3²²⁷, 126, F₃, 2, 137) (dual of [(126, 2), 25, 138]-NRT-code)	[i]
8	Linear OOA(3²²⁶, 126, F₃, 2, 136) (dual of [(126, 2), 26, 137]-NRT-code)	[i]
9	Linear OOA(3²²⁵, 125, F₃, 2, 135) (dual of [(125, 2), 25, 136]-NRT-code)	[i]
10	Linear OOA(3²²⁴, 125, F₃, 2, 134) (dual of [(125, 2), 26, 135]-NRT-code)	[i]
11	Linear OOA(3²²³, 124, F₃, 2, 133) (dual of [(124, 2), 25, 134]-NRT-code)	[i]
12	Linear OOA(3²³⁰, 64, F₃, 4, 140) (dual of [(64, 4), 26, 141]-NRT-code)	[i]		OOA Folding