MinT - Information on Result #895106

Information on Result #895106

Linear OOA(3¹⁸⁷, 4783019, F₃, 2, 14) (dual of [(4783019, 2), 9565851, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3¹⁷, 43, F₃, 2, 7) (dual of [(43, 2), 69, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁷, 86, F₃, 7) (dual of [86, 69, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁷, 87, F₃, 7) (dual of [87, 70, 8]-code), using
    - extended or lengthened subfield codes of Reedâ€“Solomon codes [i]
linear OOA(3¹⁷⁰, 4782976, F₃, 2, 14) (dual of [(4782976, 2), 9565782, 15]-NRT-code), using
- trace code [i] based on linear OOA(9⁸⁵, 2391488, F₉, 2, 14) (dual of [(2391488, 2), 4782891, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(9⁸⁵, 4782976, F₉, 14) (dual of [4782976, 4782891, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
      1. 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]
      2. linear OA(9⁷⁸, 4782969, F₉, 13) (dual of [4782969, 4782891, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. 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.