MinT - Information on Result #2610943

Information on Result #2610943

Linear OOA(2⁹², 36, F₂, 3, 52) (dual of [(36, 3), 16, 53]-NRT-code), using strength reduction based on linear OOA(2⁹², 36, F₂, 3, 53) (dual of [(36, 3), 16, 54]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁸, 12, F₁₆, 8) (dual of [12, 4, 9]-code or 12-arc in PG(7,16)), using
  - discarding factors / shortening the dual code based on linear OA(16⁸, 16, F₁₆, 8) (dual of [16, 8, 9]-code or 16-arc in PG(7,16)), using
    - Reedâ€“Solomon code RS(8,16) [i]
2. linear OOA(2⁵, 3, F₂, 3, 5) (dual of [(3, 3), 4, 6]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(3;4,2) [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(2⁹³, 36, F₂, 3, 52) (dual of [(36, 3), 15, 53]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2⁹¹, 35, F₂, 3, 51) (dual of [(35, 3), 14, 52]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2⁹⁰, 35, F₂, 3, 50) (dual of [(35, 3), 15, 51]-NRT-code)	[i]
4	Linear OOA(2⁸⁹, 35, F₂, 3, 49) (dual of [(35, 3), 16, 50]-NRT-code)	[i]
5	Linear OOA(2⁸⁸, 34, F₂, 3, 48) (dual of [(34, 3), 14, 49]-NRT-code)	[i]
6	Linear OOA(2⁸⁷, 34, F₂, 3, 47) (dual of [(34, 3), 15, 48]-NRT-code)	[i]
7	Linear OOA(2⁸⁶, 34, F₂, 3, 46) (dual of [(34, 3), 16, 47]-NRT-code)	[i]
8	Linear OOA(2⁹², 18, F₂, 6, 52) (dual of [(18, 6), 16, 53]-NRT-code)	[i]	OOA Folding