MinT - Information on Result #1685317

Information on Result #1685317

Linear OOA(2²⁰³, 5951, F₂, 7, 27) (dual of [(5951, 7), 41454, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁰³, 5951, F₂, 5, 27) (dual of [(5951, 5), 29552, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁰³, 6561, F₂, 5, 27) (dual of [(6561, 5), 32602, 28]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2²⁰³, 32805, F₂, 27) (dual of [32805, 32602, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
    1. linear OA(2¹⁹⁶, 32768, F₂, 27) (dual of [32768, 32572, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(2¹⁶⁶, 32768, F₂, 23) (dual of [32768, 32602, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    3. linear OA(2⁷, 37, F₂, 3) (dual of [37, 30, 4]-code or 37-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: 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(2²⁰³, 2975, F₂, 35, 27) (dual of [(2975, 35), 103922, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row