MinT - Information on Result #2243380

Information on Result #2243380

Linear OA(4²⁵⁵, 309, F₄, 136) (dual of [309, 54, 137]-code), using 3 times truncation based on linear OA(4²⁵⁸, 312, F₄, 139) (dual of [312, 54, 140]-code), using

concatenation of two codes [i] based on
1. linear OA(64³⁴, 52, F₆₄, 34) (dual of [52, 18, 35]-code or 52-arc in PG(33,64)), using
  - discarding factors / shortening the dual code based on linear OA(64³⁴, 64, F₆₄, 34) (dual of [64, 30, 35]-code or 64-arc in PG(33,64)), using
    - Reedâ€“Solomon code RS(30,64) [i]
2. 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		Method
1	Linear OA(4²⁵⁹, 313, F₄, 136) (dual of [313, 54, 137]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(4²⁶⁰, 314, F₄, 136) (dual of [314, 54, 137]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(4²⁵⁸, 313, F₄, 136) (dual of [313, 55, 137]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
4	Linear OA(4²⁶⁰, 316, F₄, 136) (dual of [316, 56, 137]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OOA(4²⁵⁵, 154, F₄, 2, 136) (dual of [(154, 2), 53, 137]-NRT-code)	[i]	OOA Folding
6	Linear OOA(4²⁵⁵, 103, F₄, 3, 136) (dual of [(103, 3), 54, 137]-NRT-code)	[i]	OOA Folding