MinT - Information on Result #917864

Information on Result #917864

Linear OOA(4¹²⁶, 76, F₄, 2, 74) (dual of [(76, 2), 26, 75]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(16²⁵, 19, F₁₆, 2, 24) (dual of [(19, 2), 13, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16²⁵, 24, F₁₆, 2, 24) (dual of [(24, 2), 23, 25]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,23P) [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(4¹²⁶, 76, F₄, 2, 73) (dual of [(76, 2), 26, 74]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4¹²⁶, 76, F₄, 2, 72) (dual of [(76, 2), 26, 73]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(4¹²⁷, 76, F₄, 2, 74) (dual of [(76, 2), 25, 75]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(4¹²⁵, 75, F₄, 2, 73) (dual of [(75, 2), 25, 74]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(4¹²⁴, 75, F₄, 2, 72) (dual of [(75, 2), 26, 73]-NRT-code)	[i]
6	Linear OOA(4¹²³, 74, F₄, 2, 71) (dual of [(74, 2), 25, 72]-NRT-code)	[i]
7	Linear OOA(4¹²², 74, F₄, 2, 70) (dual of [(74, 2), 26, 71]-NRT-code)	[i]
8	Linear OOA(4¹²¹, 73, F₄, 2, 69) (dual of [(73, 2), 25, 70]-NRT-code)	[i]
9	Linear OOA(4¹²⁰, 73, F₄, 2, 68) (dual of [(73, 2), 26, 69]-NRT-code)	[i]