MinT - Information on Result #1159541

Information on Result #1159541

Linear OOA(2¹⁶², 1398230, F₂, 7, 12) (dual of [(1398230, 7), 9787448, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁴, 130, F₂, 7, 6) (dual of [(130, 7), 886, 7]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(2²⁴, 130, F₂, 6, 6) (dual of [(130, 6), 756, 7]-NRT-code), using
  - appending kth column [i] based on linear OOA(2²⁴, 130, F₂, 5, 6) (dual of [(130, 5), 626, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2³, 3, F₂, 5, 3) (dual of [(3, 5), 12, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(5;12,2) [i]
      2. linear OOA(2²¹, 127, F₂, 5, 6) (dual of [(127, 5), 614, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
        linear code embedding found in a computer search [i]
linear OOA(2¹³⁸, 1398100, F₂, 7, 12) (dual of [(1398100, 7), 9786562, 13]-NRT-code), using
- OA 6-folding and stacking [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		This result only	Method
1	Linear OOA(2²²⁶, 2796460, F₂, 7, 12) (dual of [(2796460, 7), 19574994, 13]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs