MinT - Information on Result #2610638

Information on Result #2610638

Linear OOA(2⁸¹, 30, F₂, 3, 54) (dual of [(30, 3), 9, 55]-NRT-code), using strength reduction based on linear OOA(2⁸¹, 30, F₂, 3, 55) (dual of [(30, 3), 9, 56]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(8⁷, 10, F₈, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,8)), using
  - Denniston code D(1,8) [i]
2. linear OOA(2⁶, 3, F₂, 3, 6) (dual of [(3, 3), 3, 7]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(3;3,2) [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2⁸⁴, 31, F₂, 3, 54) (dual of [(31, 3), 9, 55]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2⁸⁷, 32, F₂, 3, 54) (dual of [(32, 3), 9, 55]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2⁸², 30, F₂, 3, 54) (dual of [(30, 3), 8, 55]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2⁸³, 30, F₂, 3, 54) (dual of [(30, 3), 7, 55]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(2⁸⁰, 29, F₂, 3, 53) (dual of [(29, 3), 7, 54]-NRT-code)	[i]	Truncation for OOAs
6	Linear OOA(2⁷⁹, 29, F₂, 3, 52) (dual of [(29, 3), 8, 53]-NRT-code)	[i]
7	Linear OOA(2⁷⁸, 29, F₂, 3, 51) (dual of [(29, 3), 9, 52]-NRT-code)	[i]
8	Linear OOA(2⁷⁷, 28, F₂, 3, 50) (dual of [(28, 3), 7, 51]-NRT-code)	[i]
9	Linear OOA(2⁷⁶, 28, F₂, 3, 49) (dual of [(28, 3), 8, 50]-NRT-code)	[i]
10	Linear OOA(2⁷⁵, 28, F₂, 3, 48) (dual of [(28, 3), 9, 49]-NRT-code)	[i]
11	Linear OOA(2⁷³, 27, F₂, 3, 46) (dual of [(27, 3), 8, 47]-NRT-code)	[i]
12	Linear OOA(2⁶⁹, 26, F₂, 3, 42) (dual of [(26, 3), 9, 43]-NRT-code)	[i]
13	Linear OOA(2⁸¹, 15, F₂, 6, 54) (dual of [(15, 6), 9, 55]-NRT-code)	[i]	OOA Folding