MinT - Information on Result #637348

Information on Result #637348

Linear OA(4²¹⁶, 270, F₄, 111) (dual of [270, 54, 112]-code), using concatenation of two codes based on

linear OA(64²⁷, 45, F₆₄, 27) (dual of [45, 18, 28]-code or 45-arc in PG(26,64)), using
- discarding factors / shortening the dual code based on linear OA(64²⁷, 64, F₆₄, 27) (dual of [64, 37, 28]-code or 64-arc in PG(26,64)), using
  - Reedâ€“Solomon code RS(37,64) [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(4²¹⁷, 271, F₄, 111) (dual of [271, 54, 112]-code)	[i]		Code Embedding in Larger Space
2	Linear OA(4²¹⁵, 269, F₄, 110) (dual of [269, 54, 111]-code)	[i]		Truncation
3	Linear OA(4²¹⁴, 268, F₄, 109) (dual of [268, 54, 110]-code)	[i]
4	Linear OA(4²¹³, 267, F₄, 108) (dual of [267, 54, 109]-code)	[i]
5	Linear OA(4²¹², 266, F₄, 107) (dual of [266, 54, 108]-code)	[i]
6	Linear OA(4²¹⁷, 272, F₄, 111) (dual of [272, 55, 112]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound
7	Linear OOA(4²¹⁶, 135, F₄, 2, 111) (dual of [(135, 2), 54, 112]-NRT-code)	[i]		OOA Folding
8	Linear OOA(4²¹⁶, 90, F₄, 3, 111) (dual of [(90, 3), 54, 112]-NRT-code)	[i]		OOA Folding