MinT - Information on Result #2767966

Information on Result #2767966

Linear OOA(2²⁵⁵, 75, F₂, 4, 132) (dual of [(75, 4), 45, 133]-NRT-code), using strength reduction based on linear OOA(2²⁵⁵, 75, F₂, 4, 135) (dual of [(75, 4), 45, 136]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁶, 25, F₃₂, 16) (dual of [25, 9, 17]-code or 25-arc in PG(15,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁶, 32, F₃₂, 16) (dual of [32, 16, 17]-code or 32-arc in PG(15,32)), using
    - Reedâ€“Solomon code RS(16,32) [i]
2. linear OOA(2⁷, 3, F₂, 4, 7) (dual of [(3, 4), 5, 8]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(4;5,2) [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(2²⁵⁹, 76, F₂, 4, 132) (dual of [(76, 4), 45, 133]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁵⁶, 75, F₂, 4, 132) (dual of [(75, 4), 44, 133]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁵⁷, 75, F₂, 4, 132) (dual of [(75, 4), 43, 133]-NRT-code)	[i]
4	Linear OOA(2²⁵⁸, 75, F₂, 4, 132) (dual of [(75, 4), 42, 133]-NRT-code)	[i]
5	Linear OOA(2²⁵⁴, 74, F₂, 4, 131) (dual of [(74, 4), 42, 132]-NRT-code)	[i]	Truncation for OOAs
6	Linear OOA(2²⁵³, 74, F₂, 4, 130) (dual of [(74, 4), 43, 131]-NRT-code)	[i]
7	Linear OOA(2²⁵², 74, F₂, 4, 129) (dual of [(74, 4), 44, 130]-NRT-code)	[i]
8	Linear OOA(2²⁵¹, 74, F₂, 4, 128) (dual of [(74, 4), 45, 129]-NRT-code)	[i]