MinT - Information on Result #1542893

Information on Result #1542893

Linear OOA(4²¹⁹, 16442, F₄, 3, 39) (dual of [(16442, 3), 49107, 40]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²¹⁹, 16442, F₄, 39) (dual of [16442, 16223, 40]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(4²¹⁸, 16440, F₄, 39) (dual of [16440, 16222, 40]-code), using
  - constructionÂ X applied to C_e(38) âŠ‚ C_e(30) [i] based on
    1. linear OA(4²⁰⁴, 16384, F₄, 39) (dual of [16384, 16180, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
    2. linear OA(4¹⁶², 16384, F₄, 31) (dual of [16384, 16222, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    3. linear OA(4¹⁴, 56, F₄, 7) (dual of [56, 42, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁴, 65, F₄, 7) (dual of [65, 51, 8]-code), using
        a â€œGraXXâ€ code from Grasslâ€™s database [i]
2. linear OA(4²¹⁸, 16441, F₄, 38) (dual of [16441, 16223, 39]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4²¹⁸Â > V_b^sâˆ’1(kâˆ’1)Â = 30608 113531 797284 601784 571884 669503 682514 497825 036595 402056 797005 343400 160583 429235 706272 965901 909484 812086 850443 715464 085123 651921 [i]
3. linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 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.