MinT - Information on Result #2619083

Information on Result #2619083

Linear OOA(2²⁴⁵, 90, F₂, 3, 136) (dual of [(90, 3), 25, 137]-NRT-code), using strength reduction based on linear OOA(2²⁴⁵, 90, F₂, 3, 139) (dual of [(90, 3), 25, 140]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(32¹³, 18, F₃₂, 13) (dual of [18, 5, 14]-code or 18-arc in PG(12,32)), using
  - discarding factors / shortening the dual code based on linear OA(32¹³, 32, F₃₂, 13) (dual of [32, 19, 14]-code or 32-arc in PG(12,32)), using
    - Reedâ€“Solomon code RS(19,32) [i]
2. linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,5P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [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(2²⁴⁴, 89, F₂, 3, 135) (dual of [(89, 3), 23, 136]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²⁴³, 89, F₂, 3, 134) (dual of [(89, 3), 24, 135]-NRT-code)	[i]
3	Linear OOA(2²⁴², 89, F₂, 3, 133) (dual of [(89, 3), 25, 134]-NRT-code)	[i]
4	Linear OOA(2²⁴¹, 88, F₂, 3, 132) (dual of [(88, 3), 23, 133]-NRT-code)	[i]
5	Linear OOA(2²⁴⁰, 88, F₂, 3, 131) (dual of [(88, 3), 24, 132]-NRT-code)	[i]
6	Linear OOA(2²³⁹, 88, F₂, 3, 130) (dual of [(88, 3), 25, 131]-NRT-code)	[i]
7	Linear OOA(2²³⁸, 87, F₂, 3, 129) (dual of [(87, 3), 23, 130]-NRT-code)	[i]
8	Linear OOA(2²³⁶, 87, F₂, 3, 127) (dual of [(87, 3), 25, 128]-NRT-code)	[i]
9	Linear OOA(2²³⁵, 86, F₂, 3, 126) (dual of [(86, 3), 23, 127]-NRT-code)	[i]
10	Linear OOA(2²⁴⁵, 45, F₂, 6, 136) (dual of [(45, 6), 25, 137]-NRT-code)	[i]	OOA Folding