MinT - Information on Result #3260873

Information on Result #3260873

Digital (47, 65, 268)-net over F₇, using 7² times duplication based on digital (45, 63, 268)-net over F₇, using

net defined by OOA [i] based on linear OOA(7⁶³, 268, F₇, 18, 18) (dual of [(268, 18), 4761, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(7⁶³, 2412, F₇, 18) (dual of [2412, 2349, 19]-code), using
  - constructionÂ XX applied to C_e(17) âŠ‚ C_e(15) âŠ‚ C_e(14) [i] based on
    1. linear OA(7⁶¹, 2401, F₇, 18) (dual of [2401, 2340, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 7⁴âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(7⁵³, 2401, F₇, 16) (dual of [2401, 2348, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 7⁴âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(7⁴⁹, 2401, F₇, 15) (dual of [2401, 2352, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 2400Â = 7⁴âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    4. linear OA(7¹, 10, F₇, 1) (dual of [10, 9, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(7¹, 342, F₇, 1) (dual of [342, 341, 2]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 342Â = 7³âˆ’1, defining interval IÂ =Â [0,0], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [i]
    5. linear OA(7⁰, 1, F₇, 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.