MinT - Information on Result #609999

Information on Result #609999

Linear OA(2⁷⁹, 81, F₂, 53) (dual of [81, 2, 54]-code), using repeating each code word 27 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		Method
1	Linear OA(2⁷⁹, 81, F₂, 52) (dual of [81, 2, 53]-code)	[i]	Strength Reduction
2	Linear OA(2⁷⁹, 81, F₂, 51) (dual of [81, 2, 52]-code)	[i]
3	Linear OA(2⁷⁹, 81, F₂, 50) (dual of [81, 2, 51]-code)	[i]
4	Linear OA(2⁷⁹, 81, F₂, 49) (dual of [81, 2, 50]-code)	[i]
5	Linear OA(2⁷⁹, 81, F₂, 48) (dual of [81, 2, 49]-code)	[i]
6	Linear OA(2⁷⁹, 81, F₂, 47) (dual of [81, 2, 48]-code)	[i]
7	Linear OA(2⁷⁹, 81, F₂, 46) (dual of [81, 2, 47]-code)	[i]
8	Linear OA(2⁷⁸, 80, F₂, 52) (dual of [80, 2, 53]-code)	[i]	Truncation
9	Linear OA(2⁷⁷, 79, F₂, 51) (dual of [79, 2, 52]-code)	[i]
10	Linear OA(2⁷⁵, 77, F₂, 49) (dual of [77, 2, 50]-code)	[i]
11	Linear OA(2⁷⁴, 76, F₂, 48) (dual of [76, 2, 49]-code)	[i]
12	Linear OA(2⁷², 74, F₂, 46) (dual of [74, 2, 47]-code)	[i]
13	Linear OA(2⁷¹, 73, F₂, 45) (dual of [73, 2, 46]-code)	[i]
14	Linear OA(2⁶⁹, 71, F₂, 43) (dual of [71, 2, 44]-code)	[i]
15	Linear OA(2⁶⁸, 70, F₂, 42) (dual of [70, 2, 43]-code)	[i]
16	Linear OA(2⁶⁶, 68, F₂, 40) (dual of [68, 2, 41]-code)	[i]
17	Linear OA(2⁶⁵, 67, F₂, 39) (dual of [67, 2, 40]-code)	[i]
18	Linear OA(2⁶³, 65, F₂, 37) (dual of [65, 2, 38]-code)	[i]
19	Linear OA(2⁶², 64, F₂, 36) (dual of [64, 2, 37]-code)	[i]
20	Linear OOA(2⁷⁹, 27, F₂, 3, 53) (dual of [(27, 3), 2, 54]-NRT-code)	[i]	OOA Folding