MinT - Information on Result #1620807

Information on Result #1620807

Linear OOA(3⁷³, 1469, F₃, 5, 14) (dual of [(1469, 5), 7272, 15]-NRT-code), using OOA 2-folding based on linear OOA(3⁷³, 2938, F₃, 3, 14) (dual of [(2938, 3), 8741, 15]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁷³, 2938, F₃, 2, 14) (dual of [(2938, 2), 5803, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁷³, 3284, F₃, 2, 14) (dual of [(3284, 2), 6495, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁷³, 6568, F₃, 14) (dual of [6568, 6495, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁷³, 6569, F₃, 14) (dual of [6569, 6496, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
        linear OA(3⁷³, 6561, F₃, 14) (dual of [6561, 6488, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(3⁶⁵, 6561, F₃, 13) (dual of [6561, 6496, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(3⁰, 8, F₃, 0) (dual of [8, 8, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.