MinT - Information on Result #1780878

Information on Result #1780878

Digital (181, 212, 123383)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²¹², 123383, F₄, 2, 31) (dual of [(123383, 2), 246554, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²¹², 131084, F₄, 2, 31) (dual of [(131084, 2), 261956, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4²¹², 262168, F₄, 31) (dual of [262168, 261956, 32]-code), using
  - constructionÂ XX applied to C_e(30) âŠ‚ C_e(28) âŠ‚ C_e(26) [i] based on
    1. linear OA(4²⁰⁸, 262144, F₄, 31) (dual of [262144, 261936, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(4¹⁹⁰, 262144, F₄, 29) (dual of [262144, 261954, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    3. linear OA(4¹⁸¹, 262144, F₄, 27) (dual of [262144, 261963, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    4. linear OA(4¹, 21, F₄, 1) (dual of [21, 20, 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]
    5. linear OA(4¹, 3, F₄, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹, 4, F₄, 1) (dual of [4, 3, 2]-code), using
        Reedâ€“Solomon code RS(3,4) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.