MinT - Information on Result #637469

Information on Result #637469

Linear OA(4²⁵⁸, 306, F₄, 143) (dual of [306, 48, 144]-code), using concatenation of two codes based on

linear OA(64³⁵, 51, F₆₄, 35) (dual of [51, 16, 36]-code or 51-arc in PG(34,64)), using
- discarding factors / shortening the dual code based on linear OA(64³⁵, 64, F₆₄, 35) (dual of [64, 29, 36]-code or 64-arc in PG(34,64)), using
  - Reedâ€“Solomon code RS(29,64) [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(4²⁵⁸, 306, F₄, 142) (dual of [306, 48, 143]-code)	[i]		Strength Reduction
2	Linear OA(4²⁵⁸, 306, F₄, 141) (dual of [306, 48, 142]-code)	[i]
3	Linear OA(4²⁵⁸, 306, F₄, 140) (dual of [306, 48, 141]-code)	[i]
4	Linear OA(4²⁵⁹, 307, F₄, 143) (dual of [307, 48, 144]-code)	[i]		Code Embedding in Larger Space
5	Linear OA(4²⁶⁰, 308, F₄, 143) (dual of [308, 48, 144]-code)	[i]		Code Embedding in Larger Space
6	Linear OA(4²⁵⁷, 305, F₄, 142) (dual of [305, 48, 143]-code)	[i]		Truncation
7	Linear OA(4²⁵⁶, 304, F₄, 141) (dual of [304, 48, 142]-code)	[i]
8	Linear OA(4²⁵⁵, 303, F₄, 140) (dual of [303, 48, 141]-code)	[i]
9	Linear OA(4²⁵⁴, 302, F₄, 139) (dual of [302, 48, 140]-code)	[i]
10	Linear OA(4²⁵³, 301, F₄, 138) (dual of [301, 48, 139]-code)	[i]
11	Linear OA(4²⁵¹, 299, F₄, 136) (dual of [299, 48, 137]-code)	[i]
12	Linear OOA(4²⁵⁸, 153, F₄, 2, 143) (dual of [(153, 2), 48, 144]-NRT-code)	[i]		OOA Folding
13	Linear OOA(4²⁵⁸, 102, F₄, 3, 143) (dual of [(102, 3), 48, 144]-NRT-code)	[i]		OOA Folding