MinT - Information on Result #1682696

Information on Result #1682696

Linear OOA(2¹⁶³, 4105, F₂, 7, 22) (dual of [(4105, 7), 28572, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶³, 4105, F₂, 4, 22) (dual of [(4105, 4), 16257, 23]-NRT-code), using

OOA 4-folding [i] based on linear OA(2¹⁶³, 16420, F₂, 22) (dual of [16420, 16257, 23]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2¹⁶¹, 16418, F₂, 22) (dual of [16418, 16257, 23]-code), using
  - 1 times truncation [i] based on linear OA(2¹⁶², 16419, F₂, 23) (dual of [16419, 16257, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
      1. linear OA(2¹⁵⁵, 16384, F₂, 23) (dual of [16384, 16229, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(2¹²⁷, 16384, F₂, 19) (dual of [16384, 16257, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(2¹⁶⁴, 4105, F₂, 7, 22) (dual of [(4105, 7), 28571, 23]-NRT-code)	[i]		OOA Duplication