MinT - Information on Result #1097493

Information on Result #1097493

Linear OOA(2²¹¹, 418, F₂, 5, 37) (dual of [(418, 5), 1879, 38]-NRT-code), using OOA 5-folding based on linear OA(2²¹¹, 2090, F₂, 37) (dual of [2090, 1879, 38]-code), using

discarding factors / shortening the dual code based on linear OA(2²¹¹, 2093, F₂, 37) (dual of [2093, 1882, 38]-code), using
- constructionÂ X applied to C_e(36) âŠ‚ C_e(30) [i] based on
  1. linear OA(2¹⁹⁹, 2048, F₂, 37) (dual of [2048, 1849, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
  2. linear OA(2¹⁶⁶, 2048, F₂, 31) (dual of [2048, 1882, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
  3. linear OA(2¹², 45, F₂, 5) (dual of [45, 33, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹², 48, F₂, 5) (dual of [48, 36, 6]-code), using
      - adding a parity check bit [i] based on linear OA(2¹¹, 47, F₂, 4) (dual of [47, 36, 5]-code), using
        extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F₂, using
        linear code embedding found in a computer search [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(2²¹¹, 418, F₂, 5, 36) (dual of [(418, 5), 1879, 37]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²¹², 418, F₂, 5, 37) (dual of [(418, 5), 1878, 38]-NRT-code)	[i]		OOA Duplication