MinT - Information on Result #917886

Information on Result #917886

Linear OOA(4¹³⁸, 80, F₄, 2, 86) (dual of [(80, 2), 22, 87]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(16²⁹, 20, F₁₆, 2, 28) (dual of [(20, 2), 11, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16²⁹, 24, F₁₆, 2, 28) (dual of [(24, 2), 19, 29]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,19P) [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(4², 4, F₄, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,4)), using
- Reedâ€“Solomon code RS(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(4¹³⁸, 80, F₄, 2, 85) (dual of [(80, 2), 22, 86]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4¹³⁸, 80, F₄, 2, 84) (dual of [(80, 2), 22, 85]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(4¹³⁷, 79, F₄, 2, 85) (dual of [(79, 2), 21, 86]-NRT-code)	[i]		Truncation for OOAs
4	Linear OOA(4¹³⁶, 79, F₄, 2, 84) (dual of [(79, 2), 22, 85]-NRT-code)	[i]
5	Linear OOA(4¹³⁵, 78, F₄, 2, 83) (dual of [(78, 2), 21, 84]-NRT-code)	[i]
6	Linear OOA(4¹³⁴, 78, F₄, 2, 82) (dual of [(78, 2), 22, 83]-NRT-code)	[i]
7	Linear OOA(4¹³³, 77, F₄, 2, 81) (dual of [(77, 2), 21, 82]-NRT-code)	[i]
8	Linear OOA(4¹³², 77, F₄, 2, 80) (dual of [(77, 2), 22, 81]-NRT-code)	[i]
9	Linear OOA(4¹³¹, 76, F₄, 2, 79) (dual of [(76, 2), 21, 80]-NRT-code)	[i]