MinT - Information on Result #1535481

Information on Result #1535481

Linear OOA(4¹⁰¹, 32778, F₄, 3, 17) (dual of [(32778, 3), 98233, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁰¹, 32778, F₄, 2, 17) (dual of [(32778, 2), 65455, 18]-NRT-code), using

OOA 2-folding [i] based on linear OA(4¹⁰¹, 65556, F₄, 17) (dual of [65556, 65455, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹⁰¹, 65557, F₄, 17) (dual of [65557, 65456, 18]-code), using
  - constructionÂ XX applied to C_e(16) âŠ‚ C_e(13) âŠ‚ C_e(12) [i] based on
    1. linear OA(4⁹⁷, 65536, F₄, 17) (dual of [65536, 65439, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    2. linear OA(4⁸¹, 65536, F₄, 14) (dual of [65536, 65455, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
    3. linear OA(4⁷³, 65536, F₄, 13) (dual of [65536, 65463, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    4. linear OA(4³, 20, F₄, 2) (dual of [20, 17, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(4³, 21, F₄, 2) (dual of [21, 18, 3]-code), using
        Hamming code H(3,4) [i]
    5. linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code), using
      - dual of repetition code with length 1 [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.