MinT - Information on Result #637262

Information on Result #637262

Linear OA(4¹²⁹, 150, F₄, 75) (dual of [150, 21, 76]-code), using concatenation of two codes based on

linear OA(64¹⁸, 25, F₆₄, 18) (dual of [25, 7, 19]-code or 25-arc in PG(17,64)), using
- discarding factors / shortening the dual code based on linear OA(64¹⁸, 64, F₆₄, 18) (dual of [64, 46, 19]-code or 64-arc in PG(17,64)), using
  - Reedâ€“Solomon code RS(46,64) [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(4¹²⁹, 150, F₄, 74) (dual of [150, 21, 75]-code)	[i]		Strength Reduction
2	Linear OA(4¹³⁰, 151, F₄, 75) (dual of [151, 21, 76]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹²⁸, 149, F₄, 74) (dual of [149, 21, 75]-code)	[i]		Truncation
4	Linear OA(4¹²⁷, 148, F₄, 73) (dual of [148, 21, 74]-code)	[i]
5	Linear OA(4¹²⁶, 147, F₄, 72) (dual of [147, 21, 73]-code)	[i]
6	Linear OA(4¹²⁵, 146, F₄, 71) (dual of [146, 21, 72]-code)	[i]
7	Linear OA(4¹²⁴, 145, F₄, 70) (dual of [145, 21, 71]-code)	[i]
8	Linear OOA(4¹²⁹, 75, F₄, 2, 75) (dual of [(75, 2), 21, 76]-NRT-code)	[i]		OOA Folding
9	Linear OOA(4¹²⁹, 50, F₄, 3, 75) (dual of [(50, 3), 21, 76]-NRT-code)	[i]		OOA Folding