MinT - Information on Result #1719089

Information on Result #1719089

Linear OOA(4¹⁸⁷, 155535, F₄, 27, 23) (dual of [(155535, 27), 4199258, 24]-NRT-code), using OOA 4-folding and stacking with additional row based on linear OOA(4¹⁸⁷, 622141, F₄, 3, 23) (dual of [(622141, 3), 1866236, 24]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁸⁷, 622144, F₄, 3, 23) (dual of [(622144, 3), 1866245, 24]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹⁸⁷, 622144, F₄, 23) (dual of [622144, 621957, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁸⁷, 1048623, F₄, 23) (dual of [1048623, 1048436, 24]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(4¹⁸¹, 1048577, F₄, 25) (dual of [1048577, 1048396, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      2. linear OA(4¹⁴¹, 1048577, F₄, 19) (dual of [1048577, 1048436, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(4⁶, 46, F₄, 3) (dual of [46, 40, 4]-code or 46-cap in PG(5,4)), using
        discarding factors / shortening the dual code based on linear OA(4⁶, 102, F₄, 3) (dual of [102, 96, 4]-code or 102-cap in PG(5,4)), using
        large caps in PG(5,Â b) [i]

Mode: Linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (164, 187, 155535)-net over F₄	[i]		Net Defined by OOA