MinT - Information on Result #2611730

Information on Result #2611730

Linear OOA(2¹¹⁵, 45, F₂, 3, 64) (dual of [(45, 3), 20, 65]-NRT-code), using strength reduction based on linear OOA(2¹¹⁵, 45, F₂, 3, 65) (dual of [(45, 3), 20, 66]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16¹⁰, 15, F₁₆, 10) (dual of [15, 5, 11]-code or 15-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(2¹¹⁶, 45, F₂, 3, 64) (dual of [(45, 3), 19, 65]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹¹⁴, 44, F₂, 3, 63) (dual of [(44, 3), 18, 64]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(2¹¹³, 44, F₂, 3, 62) (dual of [(44, 3), 19, 63]-NRT-code)	[i]
4	Linear OOA(2¹¹², 44, F₂, 3, 61) (dual of [(44, 3), 20, 62]-NRT-code)	[i]
5	Linear OOA(2¹¹¹, 43, F₂, 3, 60) (dual of [(43, 3), 18, 61]-NRT-code)	[i]
6	Linear OOA(2¹¹⁰, 43, F₂, 3, 59) (dual of [(43, 3), 19, 60]-NRT-code)	[i]
7	Linear OOA(2¹⁰⁹, 43, F₂, 3, 58) (dual of [(43, 3), 20, 59]-NRT-code)	[i]
8	Linear OOA(2²⁴³, 84, F₂, 3, 128) (dual of [(84, 3), 9, 129]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
9	Linear OOA(2²⁴⁴, 84, F₂, 3, 129) (dual of [(84, 3), 8, 130]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs