MinT - Information on Result #1181847

Information on Result #1181847

Linear OOA(2¹⁶⁷, 6557, F₂, 20, 20) (dual of [(6557, 20), 130973, 21]-NRT-code), using OA 10-folding and stacking based on linear OA(2¹⁶⁷, 65570, F₂, 20) (dual of [65570, 65403, 21]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁶⁷, 65575, F₂, 20) (dual of [65575, 65408, 21]-code), using
- 1 times truncation [i] based on linear OA(2¹⁶⁸, 65576, F₂, 21) (dual of [65576, 65408, 22]-code), using
  - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
    1. linear OA(2¹⁶¹, 65537, F₂, 21) (dual of [65537, 65376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    2. linear OA(2¹²⁹, 65537, F₂, 17) (dual of [65537, 65408, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 2³²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    3. linear OA(2⁷, 39, F₂, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
      - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]

Mode: Constructive and 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 (147, 167, 6557)-net over F₂	[i]		Net Defined by OOA