MinT - Information on Result #1152160

Information on Result #1152160

Linear OOA(2²¹⁷, 4686, F₂, 7, 28) (dual of [(4686, 7), 32585, 29]-NRT-code), using OOA 7-folding based on linear OA(2²¹⁷, 32802, F₂, 28) (dual of [32802, 32585, 29]-code), using

discarding factors / shortening the dual code based on linear OA(2²¹⁷, 32805, F₂, 28) (dual of [32805, 32588, 29]-code), using
- 1 times truncation [i] based on linear OA(2²¹⁸, 32806, F₂, 29) (dual of [32806, 32588, 30]-code), using
  - constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(2²¹¹, 32769, F₂, 29) (dual of [32769, 32558, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 2³⁰âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
    2. linear OA(2¹⁸¹, 32769, F₂, 25) (dual of [32769, 32588, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 2³⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    3. linear OA(2⁷, 37, F₂, 3) (dual of [37, 30, 4]-code or 37-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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²¹⁹, 4686, F₂, 7, 28) (dual of [(4686, 7), 32583, 29]-NRT-code)	[i]		OOA Duplication