MinT - Information on Result #2611551

Information on Result #2611551

Linear OOA(2¹¹⁰, 42, F₂, 3, 64) (dual of [(42, 3), 16, 65]-NRT-code), using strength reduction based on linear OOA(2¹¹⁰, 42, F₂, 3, 65) (dual of [(42, 3), 16, 66]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁰, 14, F₁₆, 10) (dual of [14, 4, 11]-code or 14-arc in PG(9,16)), using
  - discarding factors / shortening the dual code based on linear OA(16¹⁰, 16, F₁₆, 10) (dual of [16, 6, 11]-code or 16-arc in PG(9,16)), using
    - Reedâ€“Solomon code RS(6,16) [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(2¹¹¹, 42, F₂, 3, 64) (dual of [(42, 3), 15, 65]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁰⁹, 41, F₂, 3, 63) (dual of [(41, 3), 14, 64]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2¹⁰⁸, 41, F₂, 3, 62) (dual of [(41, 3), 15, 63]-NRT-code)	[i]
4	Linear OOA(2¹⁰⁷, 41, F₂, 3, 61) (dual of [(41, 3), 16, 62]-NRT-code)	[i]
5	Linear OOA(2¹⁰⁶, 40, F₂, 3, 60) (dual of [(40, 3), 14, 61]-NRT-code)	[i]
6	Linear OOA(2¹⁰⁵, 40, F₂, 3, 59) (dual of [(40, 3), 15, 60]-NRT-code)	[i]
7	Linear OOA(2¹⁰⁴, 40, F₂, 3, 58) (dual of [(40, 3), 16, 59]-NRT-code)	[i]
8	Linear OOA(2¹⁰³, 39, F₂, 3, 57) (dual of [(39, 3), 14, 58]-NRT-code)	[i]
9	Linear OOA(2¹⁰², 39, F₂, 3, 56) (dual of [(39, 3), 15, 57]-NRT-code)	[i]
10	Linear OOA(2¹¹⁰, 21, F₂, 6, 64) (dual of [(21, 6), 16, 65]-NRT-code)	[i]	OOA Folding