MinT - Information on Result #1081211

Information on Result #1081211

Linear OOA(3²²⁴, 4194352, F₃, 4, 15) (dual of [(4194352, 4), 16777184, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶¹, 2796200, F₃, 4, 7) (dual of [(2796200, 4), 11184739, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3⁶¹, 8388601, F₃, 7) (dual of [8388601, 8388540, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁶¹, large, F₃, 7) (dual of [large, large−61, 8]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
linear OOA(3¹⁶³, 2097176, F₃, 4, 15) (dual of [(2097176, 4), 8388541, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹³, 26, F₃, 4, 7) (dual of [(26, 4), 91, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (6, 13, 26)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹⁵⁰, 2097150, F₃, 4, 15) (dual of [(2097150, 4), 8388450, 16]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(3¹⁵⁰, 8388600, F₃, 15) (dual of [8388600, 8388450, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁵⁰, large, F₃, 15) (dual of [large, large−150, 16]-code), using
        the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

None.