MinT - Information on Result #1486687

Information on Result #1486687

Linear OOA(7⁴³, 2407, F₇, 3, 11) (dual of [(2407, 3), 7178, 12]-NRT-code), using OOA 2-folding based on linear OOA(7⁴³, 4814, F₇, 2, 11) (dual of [(4814, 2), 9585, 12]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(7⁴³, 4815, F₇, 2, 11) (dual of [(4815, 2), 9587, 12]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(7⁴³, 4815, F₇, 11) (dual of [4815, 4772, 12]-code), using
  - 8 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 7 times 0) [i] based on linear OA(7⁴², 4806, F₇, 11) (dual of [4806, 4764, 12]-code), using
    - trace code [i] based on linear OA(49²¹, 2403, F₄₉, 11) (dual of [2403, 2382, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        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]
        linear OA(49¹⁹, 2401, F₄₉, 10) (dual of [2401, 2382, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 49²âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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, 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.