MinT - Information on Result #1096273

Information on Result #1096273

Linear OOA(2¹⁶³, 3284, F₂, 5, 23) (dual of [(3284, 5), 16257, 24]-NRT-code), using OOA 5-folding based on linear OA(2¹⁶³, 16420, F₂, 23) (dual of [16420, 16257, 24]-code), using

1 times code embedding in larger space [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: 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		Method
1	Linear OOA(2¹⁶⁴, 3284, F₂, 5, 23) (dual of [(3284, 5), 16256, 24]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁶⁵, 3284, F₂, 5, 23) (dual of [(3284, 5), 16255, 24]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁶², 3283, F₂, 5, 22) (dual of [(3283, 5), 16253, 23]-NRT-code)	[i]	Truncation for OOAs