MinT - Information on Result #1081324

Information on Result #1081324

Linear OOA(3²⁴³, 2391510, F₃, 4, 18) (dual of [(2391510, 4), 9565797, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁹, 26, F₃, 4, 9) (dual of [(26, 4), 85, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁶, 14, F₃, 4, 4) (dual of [(14, 4), 50, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(3⁶, 14, F₃, 3, 4) (dual of [(14, 3), 36, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (2, 6, 14)-net over F₃, using
        linear code embedding found in a computer search [i]
  2. linear OOA(3¹³, 13, F₃, 4, 9) (dual of [(13, 4), 39, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 13, 13)-net over F₃, using
      - a shift-net [i]
linear OOA(3²²⁴, 2391484, F₃, 4, 18) (dual of [(2391484, 4), 9565712, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3²²⁴, 4782968, F₃, 2, 18) (dual of [(4782968, 2), 9565712, 19]-NRT-code), using
  - trace code [i] based on linear OOA(9¹¹², 2391484, F₉, 2, 18) (dual of [(2391484, 2), 4782856, 19]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(9¹¹², 4782968, F₉, 18) (dual of [4782968, 4782856, 19]-code), using
      - discarding factors / shortening the dual code based on linear OA(9¹¹², 4782969, F₉, 18) (dual of [4782969, 4782857, 19]-code), using
        1 times truncation [i] based on linear OA(9¹¹³, 4782970, F₉, 19) (dual of [4782970, 4782857, 20]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 9¹⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.