MinT - Information on Result #1052771

Information on Result #1052771

Linear OOA(2¹⁹⁵, 32778, F₂, 4, 23) (dual of [(32778, 4), 130917, 24]-NRT-code), using OOA 4-folding based on linear OA(2¹⁹⁵, 131112, F₂, 23) (dual of [131112, 130917, 24]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁹⁵, 131113, F₂, 23) (dual of [131113, 130918, 24]-code), using
- constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
  1. linear OA(2¹⁸⁸, 131072, F₂, 23) (dual of [131072, 130884, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  2. linear OA(2¹⁵⁴, 131072, F₂, 19) (dual of [131072, 130918, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  3. linear OA(2⁷, 41, F₂, 3) (dual of [41, 34, 4]-code or 41-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(2¹⁹⁵, 32778, F₂, 4, 22) (dual of [(32778, 4), 130917, 23]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁹⁶, 32778, F₂, 4, 23) (dual of [(32778, 4), 130916, 24]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁹⁷, 32778, F₂, 4, 23) (dual of [(32778, 4), 130915, 24]-NRT-code)	[i]	OOA Duplication