MinT - Information on Result #1132175

Information on Result #1132175

Linear OOA(2²²⁸, 174770, F₂, 6, 23) (dual of [(174770, 6), 1048392, 24]-NRT-code), using OOA 6-folding based on linear OA(2²²⁸, 1048620, F₂, 23) (dual of [1048620, 1048392, 24]-code), using

discarding factors / shortening the dual code based on linear OA(2²²⁸, 1048623, F₂, 23) (dual of [1048623, 1048395, 24]-code), using
- constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
  1. linear OA(2²²¹, 1048576, F₂, 23) (dual of [1048576, 1048355, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  2. linear OA(2¹⁸¹, 1048576, F₂, 19) (dual of [1048576, 1048395, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 2²⁰âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  3. linear OA(2⁷, 47, F₂, 3) (dual of [47, 40, 4]-code or 47-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(2²²⁸, 174770, F₂, 6, 22) (dual of [(174770, 6), 1048392, 23]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²²⁹, 174770, F₂, 6, 23) (dual of [(174770, 6), 1048391, 24]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²³⁰, 174770, F₂, 6, 23) (dual of [(174770, 6), 1048390, 24]-NRT-code)	[i]	OOA Duplication