MinT - Information on Result #1725272

Information on Result #1725272

Digital (39, 52, 2427)-net over F₇, using net defined by OOA based on linear OOA(7⁵², 2427, F₇, 15, 13) (dual of [(2427, 15), 36353, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(7⁵², 4855, F₇, 3, 13) (dual of [(4855, 3), 14513, 14]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7⁵², 4855, F₇, 13) (dual of [4855, 4803, 14]-code), using
  - 47 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 5 times 0, 1, 40 times 0) [i] based on linear OA(7⁵⁰, 4806, F₇, 13) (dual of [4806, 4756, 14]-code), using
    - trace code [i] based on linear OA(49²⁵, 2403, F₄₉, 13) (dual of [2403, 2378, 14]-code), using
      - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        linear OA(49²⁵, 2401, F₄₉, 13) (dual of [2401, 2376, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        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]
        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, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.