MinT - Information on Result #637227

Information on Result #637227

Linear OA(4⁸⁷, 102, F₄, 51) (dual of [102, 15, 52]-code), using concatenation of two codes based on

linear OA(64¹², 17, F₆₄, 12) (dual of [17, 5, 13]-code or 17-arc in PG(11,64)), using
- discarding factors / shortening the dual code based on linear OA(64¹², 64, F₆₄, 12) (dual of [64, 52, 13]-code or 64-arc in PG(11,64)), using
  - Reedâ€“Solomon code RS(52,64) [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, 102, F₄, 50) (dual of [102, 15, 51]-code)	[i]		Strength Reduction
2	Linear OA(4⁸⁸, 103, F₄, 51) (dual of [103, 15, 52]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4⁸⁶, 101, F₄, 50) (dual of [101, 15, 51]-code)	[i]		Truncation
4	Linear OA(4⁸⁵, 100, F₄, 49) (dual of [100, 15, 50]-code)	[i]
5	Linear OA(4⁸⁴, 99, F₄, 48) (dual of [99, 15, 49]-code)	[i]
6	Linear OOA(4⁸⁷, 51, F₄, 2, 51) (dual of [(51, 2), 15, 52]-NRT-code)	[i]		OOA Folding
7	Linear OOA(4⁸⁷, 34, F₄, 3, 51) (dual of [(34, 3), 15, 52]-NRT-code)	[i]		OOA Folding