MinT - Information on Result #1545837

Information on Result #1545837

Linear OOA(4²⁵⁰, 16447, F₄, 3, 45) (dual of [(16447, 3), 49091, 46]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4²⁵⁰, 16447, F₄, 45) (dual of [16447, 16197, 46]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(4²⁴⁶, 16440, F₄, 45) (dual of [16440, 16194, 46]-code), using
  - constructionÂ X applied to C_e(44) âŠ‚ C_e(36) [i] based on
    1. linear OA(4²³², 16384, F₄, 45) (dual of [16384, 16152, 46]-code), using an extension C_e(44) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,44], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 45 [i]
    2. linear OA(4¹⁹⁰, 16384, F₄, 37) (dual of [16384, 16194, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 4⁷âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [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(4²⁴⁶, 16443, F₄, 43) (dual of [16443, 16197, 44]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4²⁴⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 86 919859 693534 699858 603338 551172 944189 456016 780443 047038 723555 346524 679859 857964 165522 152943 794079 070793 308453 658832 487562 688969 010691 787884 880008 [i]
3. linear OA(4¹, 4, F₄, 1) (dual of [4, 3, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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.