MinT - Information on Result #1608693

Information on Result #1608693

Linear OOA(3²⁰¹, 1294104, F₃, 4, 21) (dual of [(1294104, 4), 5176215, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁰¹, 1294104, F₃, 3, 21) (dual of [(1294104, 3), 3882111, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁰¹, 1594334, F₃, 3, 21) (dual of [(1594334, 3), 4782801, 22]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²⁰⁰, 1594334, F₃, 3, 21) (dual of [(1594334, 3), 4782802, 22]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²⁰⁰, 4783002, F₃, 21) (dual of [4783002, 4782802, 22]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(3¹⁹⁸, 4783000, F₃, 21) (dual of [4783000, 4782802, 22]-code), using
      - constructionÂ X4 applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
        linear OA(3¹⁹⁷, 4782970, F₃, 21) (dual of [4782970, 4782773, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
        linear OA(3¹⁶⁹, 4782970, F₃, 19) (dual of [4782970, 4782801, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
        linear OA(3²⁹, 30, F₃, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
        dual of repetition code with length 30 [i]
        linear OA(3¹, 30, F₃, 1) (dual of [30, 29, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.