MinT - Information on Result #1711167

Information on Result #1711167

Linear OOA(2²⁰⁸, 3281, F₂, 35, 27) (dual of [(3281, 35), 114627, 28]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OOA(2²⁰⁸, 6563, F₂, 7, 27) (dual of [(6563, 7), 45733, 28]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2²⁰⁸, 6563, F₂, 5, 27) (dual of [(6563, 5), 32607, 28]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2²⁰⁸, 32815, F₂, 27) (dual of [32815, 32607, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁰⁸, 32816, F₂, 27) (dual of [32816, 32608, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(20) [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(2¹⁵¹, 32768, F₂, 21) (dual of [32768, 32617, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. 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: Linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (181, 208, 3281)-net over F₂	[i]		Net Defined by OOA