MinT - Information on Result #1115720

Information on Result #1115720

Linear OOA(2²²⁹, 3355948, F₂, 5, 13) (dual of [(3355948, 5), 16779511, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁴, 2097149, F₂, 5, 6) (dual of [(2097149, 5), 10485681, 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(2¹⁶⁵, 1677974, F₂, 5, 13) (dual of [(1677974, 5), 8389705, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁶, 254, F₂, 5, 6) (dual of [(254, 5), 1244, 7]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2²⁶, 255, F₂, 3, 6) (dual of [(255, 3), 739, 7]-NRT-code), using
      - strength reduction [i] based on linear OOA(2²⁶, 255, F₂, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
        OOAs constructed from BCH codes [i]
  2. linear OOA(2¹³⁹, 1677720, F₂, 5, 13) (dual of [(1677720, 5), 8388461, 14]-NRT-code), using
    - OOA 5-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		This result only	Method
1	Linear OOA(2²²⁹, 3355948, F₂, 5, 12) (dual of [(3355948, 5), 16779511, 13]-NRT-code)	[i]		Strength Reduction for OOAs