MinT - Information on Result #1621616

Information on Result #1621616

Linear OOA(3¹³⁰, 471, F₃, 5, 29) (dual of [(471, 5), 2225, 30]-NRT-code), using OOA 2-folding based on linear OOA(3¹³⁰, 942, F₃, 3, 29) (dual of [(942, 3), 2696, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹³⁰, 943, F₃, 3, 29) (dual of [(943, 3), 2699, 30]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹³⁰, 943, F₃, 29) (dual of [943, 813, 30]-code), using
  - 193 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (4, 1, 1, 1, 0, 0, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 9 times 0, 1, 12 times 0, 1, 15 times 0, 1, 19 times 0, 1, 23 times 0, 1, 26 times 0, 1, 29 times 0, 1, 31 times 0) [i] based on linear OA(3¹¹², 732, F₃, 29) (dual of [732, 620, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(27) [i] based on
      1. linear OA(3¹¹², 729, F₃, 29) (dual of [729, 617, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(3¹⁰⁹, 729, F₃, 28) (dual of [729, 620, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      3. linear OA(3⁰, 3, F₃, 0) (dual of [3, 3, 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.