MinT - Information on Result #610000

Information on Result #610000

Linear OA(2⁷⁶, 78, F₂, 51) (dual of [78, 2, 52]-code), using repeating each code word 26 times based on linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using

discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- parity-check code [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(2⁷⁶, 78, F₂, 50) (dual of [78, 2, 51]-code)	[i]		Strength Reduction
2	Linear OA(2⁷⁶, 78, F₂, 49) (dual of [78, 2, 50]-code)	[i]
3	Linear OA(2⁷⁶, 78, F₂, 48) (dual of [78, 2, 49]-code)	[i]
4	Linear OA(2⁷⁶, 78, F₂, 47) (dual of [78, 2, 48]-code)	[i]
5	Linear OA(2⁷⁶, 78, F₂, 46) (dual of [78, 2, 47]-code)	[i]
6	Linear OA(2⁷⁶, 78, F₂, 45) (dual of [78, 2, 46]-code)	[i]
7	Linear OA(2⁷⁶, 78, F₂, 44) (dual of [78, 2, 45]-code)	[i]
8	Linear OA(2⁷⁵, 77, F₂, 50) (dual of [77, 2, 51]-code)	[i]		Truncation
9	Linear OA(2⁷⁴, 76, F₂, 49) (dual of [76, 2, 50]-code)	[i]
10	Linear OA(2⁷², 74, F₂, 47) (dual of [74, 2, 48]-code)	[i]
11	Linear OA(2⁷¹, 73, F₂, 46) (dual of [73, 2, 47]-code)	[i]
12	Linear OA(2⁶⁹, 71, F₂, 44) (dual of [71, 2, 45]-code)	[i]
13	Linear OA(2⁶⁸, 70, F₂, 43) (dual of [70, 2, 44]-code)	[i]
14	Linear OA(2⁶⁶, 68, F₂, 41) (dual of [68, 2, 42]-code)	[i]
15	Linear OA(2⁶⁵, 67, F₂, 40) (dual of [67, 2, 41]-code)	[i]
16	Linear OA(2⁶³, 65, F₂, 38) (dual of [65, 2, 39]-code)	[i]
17	Linear OA(2⁶², 64, F₂, 37) (dual of [64, 2, 38]-code)	[i]
18	Linear OOA(2⁷⁶, 39, F₂, 2, 51) (dual of [(39, 2), 2, 52]-NRT-code)	[i]		OOA Folding
19	Linear OOA(2⁷⁶, 26, F₂, 3, 51) (dual of [(26, 3), 2, 52]-NRT-code)	[i]		OOA Folding