MinT - Information on Result #2611250

Information on Result #2611250

Linear OOA(2¹⁰¹, 39, F₂, 3, 58) (dual of [(39, 3), 16, 59]-NRT-code), using strength reduction based on linear OOA(2¹⁰¹, 39, F₂, 3, 59) (dual of [(39, 3), 16, 60]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16⁹, 13, F₁₆, 9) (dual of [13, 4, 10]-code or 13-arc in PG(8,16)), using
  - discarding factors / shortening the dual code based on linear OA(16⁹, 16, F₁₆, 9) (dual of [16, 7, 10]-code or 16-arc in PG(8,16)), using
    - Reedâ€“Solomon code RS(7,16) [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(2¹⁰², 39, F₂, 3, 58) (dual of [(39, 3), 15, 59]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁰⁰, 38, F₂, 3, 57) (dual of [(38, 3), 14, 58]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2⁹⁹, 38, F₂, 3, 56) (dual of [(38, 3), 15, 57]-NRT-code)	[i]
4	Linear OOA(2⁹⁸, 38, F₂, 3, 55) (dual of [(38, 3), 16, 56]-NRT-code)	[i]
5	Linear OOA(2⁹⁷, 37, F₂, 3, 54) (dual of [(37, 3), 14, 55]-NRT-code)	[i]
6	Linear OOA(2⁹⁶, 37, F₂, 3, 53) (dual of [(37, 3), 15, 54]-NRT-code)	[i]
7	Linear OOA(2⁹⁵, 37, F₂, 3, 52) (dual of [(37, 3), 16, 53]-NRT-code)	[i]
8	Linear OOA(2⁹⁴, 36, F₂, 3, 51) (dual of [(36, 3), 14, 52]-NRT-code)	[i]
9	Linear OOA(2⁹³, 36, F₂, 3, 50) (dual of [(36, 3), 15, 51]-NRT-code)	[i]