MinT - Information on Result #2767791

Information on Result #2767791

Linear OOA(2²⁵², 78, F₂, 4, 115) (dual of [(78, 4), 60, 116]-NRT-code), using strength reduction based on linear OOA(2²⁵², 78, F₂, 4, 119) (dual of [(78, 4), 60, 120]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹⁴, 26, F₃₂, 14) (dual of [26, 12, 15]-code or 26-arc in PG(13,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹⁴, 32, F₃₂, 14) (dual of [32, 18, 15]-code or 32-arc in PG(13,32)), using
    - Reedâ€“Solomon code RS(18,32) [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(2²⁵³, 78, F₂, 4, 115) (dual of [(78, 4), 59, 116]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁵⁴, 78, F₂, 4, 115) (dual of [(78, 4), 58, 116]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁵¹, 77, F₂, 4, 114) (dual of [(77, 4), 57, 115]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²⁵⁰, 77, F₂, 4, 113) (dual of [(77, 4), 58, 114]-NRT-code)	[i]
5	Linear OOA(2²⁴⁹, 77, F₂, 4, 112) (dual of [(77, 4), 59, 113]-NRT-code)	[i]
6	Linear OOA(2²⁵², 39, F₂, 8, 115) (dual of [(39, 8), 60, 116]-NRT-code)	[i]	OOA Folding