MinT - Information on Result #2783935

Information on Result #2783935

Linear OOA(2²⁵¹, 74, F₂, 4, 128) (dual of [(74, 4), 45, 129]-NRT-code), using 4 step truncation based on linear OOA(2²⁵⁵, 75, F₂, 4, 132) (dual of [(75, 4), 45, 133]-NRT-code), using

strength reduction [i] 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, 128) (dual of [(76, 4), 45, 129]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁵¹, 37, F₂, 7, 128) (dual of [(37, 7), 8, 129]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2²⁵¹, 37, F₂, 8, 128) (dual of [(37, 8), 45, 129]-NRT-code)	[i]	OOA Folding