MinT - Information on Result #2259209

Information on Result #2259209

Linear OA(2²⁴³, 262188, F₂, 26) (dual of [262188, 261945, 27]-code), using 2 times code embedding in larger space based on linear OA(2²⁴¹, 262186, F₂, 26) (dual of [262186, 261945, 27]-code), using

1 times truncation [i] based on linear OA(2²⁴², 262187, F₂, 27) (dual of [262187, 261945, 28]-code), using
- constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
  1. linear OA(2²³⁵, 262144, F₂, 27) (dual of [262144, 261909, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  2. linear OA(2¹⁹⁹, 262144, F₂, 23) (dual of [262144, 261945, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  3. linear OA(2⁷, 43, F₂, 3) (dual of [43, 36, 4]-code or 43-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(2²⁴³, 87396, F₂, 3, 26) (dual of [(87396, 3), 261945, 27]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2²⁴³, 65547, F₂, 4, 26) (dual of [(65547, 4), 261945, 27]-NRT-code)	[i]
3	Linear OOA(2²⁴³, 43698, F₂, 6, 26) (dual of [(43698, 6), 261945, 27]-NRT-code)	[i]