MinT - Information on Result #1494357

Information on Result #1494357

Linear OOA(49³¹, 2969, F₄₉, 3, 12) (dual of [(2969, 3), 8876, 13]-NRT-code), using OOA 2-folding based on linear OOA(49³¹, 5938, F₄₉, 2, 12) (dual of [(5938, 2), 11845, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(49³¹, 5939, F₄₉, 2, 12) (dual of [(5939, 2), 11847, 13]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(49³¹, 5939, F₄₉, 12) (dual of [5939, 5908, 13]-code), using
  - 3528 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 6 times 0, 1, 41 times 0, 1, 162 times 0, 1, 496 times 0, 1, 1080 times 0, 1, 1737 times 0) [i] based on linear OA(49²³, 2403, F₄₉, 12) (dual of [2403, 2380, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
      1. linear OA(49²³, 2401, F₄₉, 12) (dual of [2401, 2378, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(49²¹, 2401, F₄₉, 11) (dual of [2401, 2380, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(49⁰, 2, F₄₉, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 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.