MinT - Information on Result #1151631

Information on Result #1151631

Linear OOA(2¹⁹⁴, 18730, F₂, 7, 22) (dual of [(18730, 7), 130916, 23]-NRT-code), using OOA 7-folding based on linear OA(2¹⁹⁴, 131110, F₂, 22) (dual of [131110, 130916, 23]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁹⁴, 131112, F₂, 22) (dual of [131112, 130918, 23]-code), using
- 1 times truncation [i] 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		This result only	Method
1	Linear OOA(2¹⁹⁶, 18730, F₂, 7, 22) (dual of [(18730, 7), 130914, 23]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁹⁷, 18730, F₂, 7, 22) (dual of [(18730, 7), 130913, 23]-NRT-code)	[i]		OOA Duplication