MinT - Information on Result #637253

Information on Result #637253

Linear OA(4¹²⁶, 150, F₄, 71) (dual of [150, 24, 72]-code), using concatenation of two codes based on

linear OA(64¹⁷, 25, F₆₄, 17) (dual of [25, 8, 18]-code or 25-arc in PG(16,64)), using
- discarding factors / shortening the dual code based on linear OA(64¹⁷, 64, F₆₄, 17) (dual of [64, 47, 18]-code or 64-arc in PG(16,64)), using
  - Reedâ€“Solomon code RS(47,64) [i]
linear OA(4³, 6, F₄, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
- hyperoval in PG(2,Â 4) [i]
- the Hexacode [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(4¹²⁶, 150, F₄, 70) (dual of [150, 24, 71]-code)	[i]		Strength Reduction
2	Linear OA(4¹²⁶, 150, F₄, 69) (dual of [150, 24, 70]-code)	[i]		Strength Reduction
3	Linear OA(4¹²⁷, 151, F₄, 71) (dual of [151, 24, 72]-code)	[i]		Code Embedding in Larger Space
4	Linear OA(4¹²⁵, 149, F₄, 70) (dual of [149, 24, 71]-code)	[i]		Truncation
5	Linear OA(4¹²⁴, 148, F₄, 69) (dual of [148, 24, 70]-code)	[i]
6	Linear OA(4¹²³, 147, F₄, 68) (dual of [147, 24, 69]-code)	[i]
7	Linear OA(4¹²², 146, F₄, 67) (dual of [146, 24, 68]-code)	[i]
8	Linear OA(4¹²¹, 145, F₄, 66) (dual of [145, 24, 67]-code)	[i]
9	Linear OA(4¹¹⁹, 143, F₄, 64) (dual of [143, 24, 65]-code)	[i]
10	Linear OOA(4¹²⁶, 75, F₄, 2, 71) (dual of [(75, 2), 24, 72]-NRT-code)	[i]		OOA Folding
11	Linear OOA(4¹²⁶, 50, F₄, 3, 71) (dual of [(50, 3), 24, 72]-NRT-code)	[i]		OOA Folding