MinT - Information on Result #1143426

Information on Result #1143426

Linear OOA(2²⁰⁹, 2796210, F₂, 6, 12) (dual of [(2796210, 6), 16777051, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁴, 2097149, F₂, 6, 6) (dual of [(2097149, 6), 12582830, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁴, 2097150, F₂, 3, 6) (dual of [(2097150, 3), 6291386, 7]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]
linear OOA(2¹⁴⁵, 1398105, F₂, 6, 12) (dual of [(1398105, 6), 8388485, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OOA(2¹³⁸, 1398100, F₂, 6, 12) (dual of [(1398100, 6), 8388462, 13]-NRT-code), using
    - OOA 6-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁰⁹, 2796209, F₂, 7, 12) (dual of [(2796209, 7), 19573254, 13]-NRT-code)	[i]	OOA Stacking with Additional Row
2	Linear OOA(2²⁰⁹, 2796209, F₂, 8, 12) (dual of [(2796209, 8), 22369463, 13]-NRT-code)	[i]
3	Linear OOA(2²⁰⁹, 2796209, F₂, 18, 12) (dual of [(2796209, 18), 50331553, 13]-NRT-code)	[i]