MinT - Information on Result #1487824

Information on Result #1487824

Linear OOA(7¹⁰⁹, 1468, F₇, 3, 30) (dual of [(1468, 3), 4295, 31]-NRT-code), using OOA 2-folding based on linear OOA(7¹⁰⁹, 2936, F₇, 2, 30) (dual of [(2936, 2), 5763, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(7¹⁰⁹, 2937, F₇, 2, 30) (dual of [(2937, 2), 5765, 31]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7¹⁰⁹, 2937, F₇, 30) (dual of [2937, 2828, 31]-code), using
  - 524 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 0, 0, 1, 8 times 0, 1, 23 times 0, 1, 53 times 0, 1, 102 times 0, 1, 149 times 0, 1, 180 times 0) [i] based on linear OA(7¹⁰¹, 2405, F₇, 30) (dual of [2405, 2304, 31]-code), using
    - constructionÂ X applied to C_e(29) âŠ‚ C_e(28) [i] based on
      1. linear OA(7¹⁰¹, 2401, F₇, 30) (dual of [2401, 2300, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 7⁴âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. linear OA(7⁹⁷, 2401, F₇, 29) (dual of [2401, 2304, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 7⁴âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      3. linear OA(7⁰, 4, F₇, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 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.