MinT - Information on Result #1539404

Information on Result #1539404

Linear OOA(4¹⁷⁴, 99912, F₄, 3, 26) (dual of [(99912, 3), 299562, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁷⁴, 99912, F₄, 2, 26) (dual of [(99912, 2), 199650, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁷⁴, 131077, F₄, 2, 26) (dual of [(131077, 2), 261980, 27]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4¹⁷³, 131077, F₄, 2, 26) (dual of [(131077, 2), 261981, 27]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁷³, 262154, F₄, 26) (dual of [262154, 261981, 27]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(4¹⁷², 262153, F₄, 26) (dual of [262153, 261981, 27]-code), using
      - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
        linear OA(4¹⁷², 262144, F₄, 26) (dual of [262144, 261972, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
        linear OA(4¹⁶³, 262144, F₄, 25) (dual of [262144, 261981, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
        linear OA(4⁰, 9, F₄, 0) (dual of [9, 9, 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.