MinT - Information on Result #1712591

Information on Result #1712591

Linear OOA(3⁸⁸, 2391500, F₃, 12, 9) (dual of [(2391500, 12), 28697912, 10]-NRT-code), using OOA stacking with additional row based on linear OOA(3⁸⁸, 2391501, F₃, 4, 9) (dual of [(2391501, 4), 9565916, 10]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁸⁸, 2391501, F₃, 2, 9) (dual of [(2391501, 2), 4782914, 10]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3⁸⁶, 2391500, F₃, 2, 9) (dual of [(2391500, 2), 4782914, 10]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁸⁶, 4783000, F₃, 9) (dual of [4783000, 4782914, 10]-code), using
    - constructionÂ X4 applied to C([0,4]) âŠ‚ C([0,3]) [i] based on
      1. linear OA(3⁸⁵, 4782970, F₃, 9) (dual of [4782970, 4782885, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
      2. linear OA(3⁵⁷, 4782970, F₃, 7) (dual of [4782970, 4782913, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      3. linear OA(3²⁹, 30, F₃, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
        dual of repetition code with length 30 [i]
      4. linear OA(3¹, 30, F₃, 1) (dual of [30, 29, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (79, 88, 2391500)-net over F₃	[i]		Net Defined by OOA