MinT - Information on Result #630125

Information on Result #630125

Linear OA(2¹¹⁶, 136, F₂, 51) (dual of [136, 20, 52]-code), using concatenation of two codes based on

linear OA(16¹², 17, F₁₆, 12) (dual of [17, 5, 13]-code or 17-arc in PG(11,16)), using
- extended Reedâ€“Solomon code RS_e(5,16) [i]
linear OA(2⁴, 8, F₂, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
- Reedâ€“Muller code RM(1,3) [i]
- caps in base bÂ =Â 2 [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(2¹¹⁶, 136, F₂, 50) (dual of [136, 20, 51]-code)	[i]		Strength Reduction
2	Linear OA(2¹¹⁷, 137, F₂, 51) (dual of [137, 20, 52]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(2¹¹⁵, 135, F₂, 50) (dual of [135, 20, 51]-code)	[i]		Truncation
4	Linear OOA(2¹¹⁶, 68, F₂, 2, 51) (dual of [(68, 2), 20, 52]-NRT-code)	[i]		OOA Folding
5	Linear OOA(2¹¹⁶, 45, F₂, 3, 51) (dual of [(45, 3), 19, 52]-NRT-code)	[i]
6	Linear OOA(2¹¹⁶, 27, F₂, 5, 51) (dual of [(27, 5), 19, 52]-NRT-code)	[i]