MinT - Information on Result #1081219

Information on Result #1081219

Linear OOA(3²⁰², 2391534, F₃, 4, 15) (dual of [(2391534, 4), 9565934, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁸, 46, F₃, 4, 7) (dual of [(46, 4), 166, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵, 20, F₃, 4, 3) (dual of [(20, 4), 75, 4]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
        doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
        ovoid in PG(3,Â 3) [i]
  2. 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]
linear OOA(3¹⁸⁴, 2391488, F₃, 4, 15) (dual of [(2391488, 4), 9565768, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3¹⁸⁴, 4782976, F₃, 2, 15) (dual of [(4782976, 2), 9565768, 16]-NRT-code), using
  - trace code [i] based on linear OOA(9⁹², 2391488, F₉, 2, 15) (dual of [(2391488, 2), 4782884, 16]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(9⁹², 4782976, F₉, 15) (dual of [4782976, 4782884, 16]-code), using
      - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
        linear OA(9⁹², 4782969, F₉, 15) (dual of [4782969, 4782877, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(9⁸⁵, 4782969, F₉, 14) (dual of [4782969, 4782884, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.