MinT - Information on Result #3258324

Information on Result #3258324

Digital (162, 193, 4371)-net over F₄, using 4² times duplication based on digital (160, 191, 4371)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹⁹¹, 4371, F₄, 31, 31) (dual of [(4371, 31), 135310, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(4¹⁹¹, 65566, F₄, 31) (dual of [65566, 65375, 32]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁹¹, 65567, F₄, 31) (dual of [65567, 65376, 32]-code), using
    - constructionÂ XX applied to C_e(30) âŠ‚ C_e(26) âŠ‚ C_e(25) [i] based on
      1. linear OA(4¹⁸⁵, 65536, F₄, 31) (dual of [65536, 65351, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(4¹⁶¹, 65536, F₄, 27) (dual of [65536, 65375, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      3. linear OA(4¹⁵³, 65536, F₄, 26) (dual of [65536, 65383, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      4. linear OA(4⁵, 30, F₄, 3) (dual of [30, 25, 4]-code or 30-cap in PG(4,4)), using
        discarding factors / shortening the dual code based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [i]
      5. linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code), using
        dual of repetition code with length 1 [i]

Mode: Constructive and 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.