MinT - Information on Result #635010

Information on Result #635010

Linear OA(4¹³⁸, 150, F₄, 91) (dual of [150, 12, 92]-code), using concatenation of two codes based on

linear OA(16²⁴, 30, F₁₆, 22) (dual of [30, 6, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(16²⁴, 33, F₁₆, 22) (dual of [33, 9, 23]-code), using
  - extended algebraic-geometric code AG_e(F,10P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(4¹³⁸, 150, F₄, 90) (dual of [150, 12, 91]-code)	[i]		Strength Reduction
2	Linear OA(4¹³⁸, 150, F₄, 89) (dual of [150, 12, 90]-code)	[i]		Strength Reduction
3	Linear OA(4¹³⁷, 149, F₄, 90) (dual of [149, 12, 91]-code)	[i]		Truncation
4	Linear OA(4¹³⁶, 148, F₄, 89) (dual of [148, 12, 90]-code)	[i]
5	Linear OA(4¹³⁵, 147, F₄, 88) (dual of [147, 12, 89]-code)	[i]
6	Linear OA(4¹³⁴, 146, F₄, 87) (dual of [146, 12, 88]-code)	[i]
7	Linear OA(4¹³², 144, F₄, 85) (dual of [144, 12, 86]-code)	[i]
8	Linear OA(4¹³¹, 143, F₄, 84) (dual of [143, 12, 85]-code)	[i]
9	Linear OA(4¹³⁰, 142, F₄, 83) (dual of [142, 12, 84]-code)	[i]
10	Linear OA(4¹²⁹, 141, F₄, 82) (dual of [141, 12, 83]-code)	[i]
11	Linear OA(4¹²⁷, 139, F₄, 80) (dual of [139, 12, 81]-code)	[i]
12	Linear OOA(4¹³⁸, 75, F₄, 2, 91) (dual of [(75, 2), 12, 92]-NRT-code)	[i]		OOA Folding
13	Linear OOA(4¹³⁸, 50, F₄, 3, 91) (dual of [(50, 3), 12, 92]-NRT-code)	[i]		OOA Folding