MinT - Information on Result #1143480

Information on Result #1143480

Linear OOA(2¹⁴⁶, 1398105, F₂, 6, 13) (dual of [(1398105, 6), 8388484, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁷, 5, F₂, 6, 6) (dual of [(5, 6), 23, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(2⁷, 5, F₂, 5, 6) (dual of [(5, 5), 18, 7]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,18P) [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(2¹³⁹, 1398100, F₂, 6, 13) (dual of [(1398100, 6), 8388461, 14]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2¹³⁹, 8388600, F₂, 13) (dual of [8388600, 8388461, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²¹⁰, 2796210, F₂, 6, 13) (dual of [(2796210, 6), 16777050, 14]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁴⁶, 1398104, F₂, 7, 13) (dual of [(1398104, 7), 9786582, 14]-NRT-code)	[i]	OOA Stacking with Additional Row
3	Linear OOA(2¹⁴⁶, 1398104, F₂, 8, 13) (dual of [(1398104, 8), 11184686, 14]-NRT-code)	[i]
4	Linear OOA(2¹⁴⁶, 1398104, F₂, 18, 13) (dual of [(1398104, 18), 25165726, 14]-NRT-code)	[i]