MinT - Information on Result #637425

Information on Result #637425

Linear OA(4²⁰⁷, 228, F₄, 127) (dual of [228, 21, 128]-code), using concatenation of two codes based on

linear OA(64³¹, 38, F₆₄, 31) (dual of [38, 7, 32]-code or 38-arc in PG(30,64)), using
- discarding factors / shortening the dual code based on linear OA(64³¹, 64, F₆₄, 31) (dual of [64, 33, 32]-code or 64-arc in PG(30,64)), using
  - Reedâ€“Solomon code RS(33,64) [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(4²⁰⁷, 228, F₄, 126) (dual of [228, 21, 127]-code)	[i]		Strength Reduction
2	Linear OA(4²⁰⁷, 228, F₄, 125) (dual of [228, 21, 126]-code)	[i]		Strength Reduction
3	Linear OA(4²⁰⁸, 229, F₄, 127) (dual of [229, 21, 128]-code)	[i]		Code Embedding in Larger Space
4	Linear OA(4²⁰⁶, 227, F₄, 126) (dual of [227, 21, 127]-code)	[i]		Truncation
5	Linear OA(4²⁰⁵, 226, F₄, 125) (dual of [226, 21, 126]-code)	[i]
6	Linear OA(4²⁰⁴, 225, F₄, 124) (dual of [225, 21, 125]-code)	[i]
7	Linear OOA(4²⁰⁷, 114, F₄, 2, 127) (dual of [(114, 2), 21, 128]-NRT-code)	[i]		OOA Folding
8	Linear OOA(4²⁰⁷, 76, F₄, 3, 127) (dual of [(76, 3), 21, 128]-NRT-code)	[i]		OOA Folding