MinT - Information on Result #1590640

Information on Result #1590640

Linear OOA(2¹¹⁹, 4282, F₂, 4, 16) (dual of [(4282, 4), 17009, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹⁹, 4282, F₂, 3, 16) (dual of [(4282, 3), 12727, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹¹⁹, 5473, F₂, 3, 16) (dual of [(5473, 3), 16300, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2¹¹⁹, 16419, F₂, 16) (dual of [16419, 16300, 17]-code), using
  - 1 times truncation [i] based on linear OA(2¹²⁰, 16420, F₂, 17) (dual of [16420, 16300, 18]-code), using
    - constructionÂ X applied to C([0,8]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(2¹¹³, 16385, F₂, 17) (dual of [16385, 16272, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
      2. linear OA(2⁸⁵, 16385, F₂, 13) (dual of [16385, 16300, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      3. linear OA(2⁷, 35, F₂, 3) (dual of [35, 28, 4]-code or 35-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: 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(2¹¹⁹, 2141, F₂, 8, 16) (dual of [(2141, 8), 17009, 17]-NRT-code)	[i]		OOA Folding