MinT - Information on Result #1159734

Information on Result #1159734

Linear OOA(2²³⁴, 2396752, F₂, 7, 14) (dual of [(2396752, 7), 16777030, 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(2¹⁶⁹, 1198376, F₂, 7, 14) (dual of [(1198376, 7), 8388463, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁸, 5, F₂, 7, 7) (dual of [(5, 7), 27, 8]-NRT-code), using
    - appending kth column [i] based on linear OOA(2⁸, 5, F₂, 6, 7) (dual of [(5, 6), 22, 8]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(6;F,22P) [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(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(2²³⁴, 2396751, F₂, 8, 14) (dual of [(2396751, 8), 19173774, 15]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2²³⁴, 2396751, F₂, 21, 14) (dual of [(2396751, 21), 50331537, 15]-NRT-code)	[i]		OOA Stacking with Additional Row