MinT - Information on Result #918173

Information on Result #918173

Linear OOA(4¹⁹⁰, 100, F₄, 2, 139) (dual of [(100, 2), 10, 140]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(16³⁵, 20, F₁₆, 2, 34) (dual of [(20, 2), 5, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16³⁵, 24, F₁₆, 2, 34) (dual of [(24, 2), 13, 35]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,13P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]
linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- extended Reedâ€“Solomon code RS_e(2,4) [i]
- Simplex code S(2,4) [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(4¹⁹⁰, 100, F₄, 2, 138) (dual of [(100, 2), 10, 139]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4¹⁹⁰, 100, F₄, 2, 137) (dual of [(100, 2), 10, 138]-NRT-code)	[i]
3	Linear OOA(4¹⁹⁰, 100, F₄, 2, 136) (dual of [(100, 2), 10, 137]-NRT-code)	[i]
4	Linear OOA(4¹⁸⁹, 99, F₄, 2, 138) (dual of [(99, 2), 9, 139]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(4¹⁸⁸, 99, F₄, 2, 137) (dual of [(99, 2), 10, 138]-NRT-code)	[i]
6	Linear OOA(4¹⁸⁷, 98, F₄, 2, 136) (dual of [(98, 2), 9, 137]-NRT-code)	[i]
7	Linear OOA(4¹⁸⁶, 98, F₄, 2, 135) (dual of [(98, 2), 10, 136]-NRT-code)	[i]
8	Linear OOA(4¹⁸⁵, 97, F₄, 2, 134) (dual of [(97, 2), 9, 135]-NRT-code)	[i]
9	Linear OOA(4¹⁸⁴, 97, F₄, 2, 133) (dual of [(97, 2), 10, 134]-NRT-code)	[i]
10	Linear OOA(4¹⁸³, 96, F₄, 2, 132) (dual of [(96, 2), 9, 133]-NRT-code)	[i]
11	Linear OOA(4¹⁷⁹, 94, F₄, 2, 128) (dual of [(94, 2), 9, 129]-NRT-code)	[i]