MinT - Information on Result #1079332

Information on Result #1079332

Linear OOA(2⁹⁸, 2097155, F₂, 4, 9) (dual of [(2097155, 4), 8388522, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵, 5, F₂, 4, 4) (dual of [(5, 4), 15, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁵, 5, F₂, 3, 4) (dual of [(5, 3), 10, 5]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,10P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [i]
linear OOA(2⁹³, 2097150, F₂, 4, 9) (dual of [(2097150, 4), 8388507, 10]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2⁹³, 8388600, F₂, 9) (dual of [8388600, 8388507, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁹³, large, F₂, 9) (dual of [large, large−93, 10]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁴¹, 4194308, F₂, 4, 9) (dual of [(4194308, 4), 16777091, 10]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁴², 4194310, F₂, 4, 9) (dual of [(4194310, 4), 16777098, 10]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(2⁹⁸, 2097154, F₂, 5, 9) (dual of [(2097154, 5), 10485672, 10]-NRT-code)	[i]	OOA Stacking with Additional Row
4	Linear OOA(2⁹⁸, 2097154, F₂, 6, 9) (dual of [(2097154, 6), 12582826, 10]-NRT-code)	[i]
5	Linear OOA(2⁹⁸, 2097154, F₂, 7, 9) (dual of [(2097154, 7), 14679980, 10]-NRT-code)	[i]
6	Linear OOA(2⁹⁸, 2097154, F₂, 8, 9) (dual of [(2097154, 8), 16777134, 10]-NRT-code)	[i]