MinT - Information on Result #637221

Information on Result #637221

Linear OA(4⁸⁷, 108, F₄, 47) (dual of [108, 21, 48]-code), using concatenation of two codes based on

linear OA(64¹¹, 18, F₆₄, 11) (dual of [18, 7, 12]-code or 18-arc in PG(10,64)), using
- discarding factors / shortening the dual code based on linear OA(64¹¹, 64, F₆₄, 11) (dual of [64, 53, 12]-code or 64-arc in PG(10,64)), using
  - Reedâ€“Solomon code RS(53,64) [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(4⁸⁷, 108, F₄, 46) (dual of [108, 21, 47]-code)	[i]		Strength Reduction
2	Linear OA(4⁸⁸, 109, F₄, 47) (dual of [109, 21, 48]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4⁸⁶, 107, F₄, 46) (dual of [107, 21, 47]-code)	[i]		Truncation
4	Linear OA(4⁸⁵, 106, F₄, 45) (dual of [106, 21, 46]-code)	[i]		Truncation
5	Linear OA(4⁸⁸, 110, F₄, 47) (dual of [110, 22, 48]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound
6	Linear OOA(4⁸⁷, 54, F₄, 2, 47) (dual of [(54, 2), 21, 48]-NRT-code)	[i]		OOA Folding
7	Linear OOA(4⁸⁷, 36, F₄, 3, 47) (dual of [(36, 3), 21, 48]-NRT-code)	[i]		OOA Folding