MinT - Information on Result #1151621

Information on Result #1151621

Linear OOA(2¹⁷², 4686, F₂, 7, 22) (dual of [(4686, 7), 32630, 23]-NRT-code), using OOA 7-folding based on linear OA(2¹⁷², 32802, F₂, 22) (dual of [32802, 32630, 23]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁷², 32804, F₂, 22) (dual of [32804, 32632, 23]-code), using
- 1 times truncation [i] based on linear OA(2¹⁷³, 32805, F₂, 23) (dual of [32805, 32632, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
    1. linear OA(2¹⁶⁶, 32768, F₂, 23) (dual of [32768, 32602, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(2¹³⁶, 32768, F₂, 19) (dual of [32768, 32632, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(2¹⁷⁴, 4686, F₂, 7, 22) (dual of [(4686, 7), 32628, 23]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁷⁵, 4686, F₂, 7, 22) (dual of [(4686, 7), 32627, 23]-NRT-code)	[i]		OOA Duplication