MinT - Information on Result #1165877

Information on Result #1165877

Linear OOA(2¹⁶¹, 2052, F₂, 8, 22) (dual of [(2052, 8), 16255, 23]-NRT-code), using OOA 8-folding based on linear OA(2¹⁶¹, 16416, F₂, 22) (dual of [16416, 16255, 23]-code), using

discarding factors / shortening the dual code 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: 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(2¹⁶², 2052, F₂, 8, 22) (dual of [(2052, 8), 16254, 23]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁶³, 2052, F₂, 8, 22) (dual of [(2052, 8), 16253, 23]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁴, 2052, F₂, 8, 22) (dual of [(2052, 8), 16252, 23]-NRT-code)	[i]