MinT - Information on Result #1159736

Information on Result #1159736

Linear OOA(2²³⁶, 2396756, F₂, 7, 14) (dual of [(2396756, 7), 16777056, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁵, 2097150, F₂, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
- OOA stacking with additional row [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(2¹⁷¹, 1198378, F₂, 7, 14) (dual of [(1198378, 7), 8388475, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁰, 7, F₂, 7, 7) (dual of [(7, 7), 39, 8]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹⁰, 7, F₂, 6, 7) (dual of [(7, 6), 32, 8]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(6;F,34P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]
  2. linear OOA(2¹⁶¹, 1198371, F₂, 7, 14) (dual of [(1198371, 7), 8388436, 15]-NRT-code), using
    - OOA 7-folding [i] based on linear OA(2¹⁶¹, 8388597, F₂, 14) (dual of [8388597, 8388436, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²³⁶, 2396755, F₂, 8, 14) (dual of [(2396755, 8), 19173804, 15]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2²³⁶, 2396755, F₂, 21, 14) (dual of [(2396755, 21), 50331619, 15]-NRT-code)	[i]		OOA Stacking with Additional Row