MinT - Information on Result #1684667

Information on Result #1684667

Linear OOA(2¹⁹⁴, 4107, F₂, 7, 26) (dual of [(4107, 7), 28555, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹⁴, 4107, F₂, 4, 26) (dual of [(4107, 4), 16234, 27]-NRT-code), using

OOA 4-folding [i] based on linear OA(2¹⁹⁴, 16428, F₂, 26) (dual of [16428, 16234, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁹⁴, 16431, F₂, 26) (dual of [16431, 16237, 27]-code), using
  - 1 times truncation [i] based on linear OA(2¹⁹⁵, 16432, F₂, 27) (dual of [16432, 16237, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(20) [i] based on
      1. linear OA(2¹⁸³, 16384, F₂, 27) (dual of [16384, 16201, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      2. linear OA(2¹⁴¹, 16384, F₂, 21) (dual of [16384, 16243, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’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.

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(2¹⁹⁴, 2053, F₂, 35, 26) (dual of [(2053, 35), 71661, 27]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row