MinT - Information on Result #1580137

Information on Result #1580137

Linear OOA(3²⁰⁷, 1324, F₃, 4, 40) (dual of [(1324, 4), 5089, 41]-NRT-code), using OOA 2-folding based on linear OOA(3²⁰⁷, 2648, F₃, 2, 40) (dual of [(2648, 2), 5089, 41]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁰⁷, 2648, F₃, 40) (dual of [2648, 2441, 41]-code), using
- 430 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (4, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 7 times 0, 1, 9 times 0, 1, 12 times 0, 1, 17 times 0, 1, 21 times 0, 1, 28 times 0, 1, 34 times 0, 1, 41 times 0, 1, 48 times 0, 1, 55 times 0, 1, 61 times 0, 1, 66 times 0) [i] based on linear OA(3¹⁸⁴, 2195, F₃, 40) (dual of [2195, 2011, 41]-code), using
  - constructionÂ X applied to C_e(39) âŠ‚ C_e(37) [i] based on
    1. linear OA(3¹⁸³, 2187, F₃, 40) (dual of [2187, 2004, 41]-code), using an extension C_e(39) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,39], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 40 [i]
    2. linear OA(3¹⁷⁶, 2187, F₃, 38) (dual of [2187, 2011, 39]-code), using an extension C_e(37) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,37], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
    3. linear OA(3¹, 8, F₃, 1) (dual of [8, 7, 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.