MinT - Information on Result #1705046

Information on Result #1705046

Linear OOA(2²³⁶, 4107, F₂, 8, 32) (dual of [(4107, 8), 32620, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³⁶, 4107, F₂, 4, 32) (dual of [(4107, 4), 16192, 33]-NRT-code), using

OOA 4-folding [i] based on linear OA(2²³⁶, 16428, F₂, 32) (dual of [16428, 16192, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2²³⁶, 16431, F₂, 32) (dual of [16431, 16195, 33]-code), using
  - 1 times truncation [i] based on linear OA(2²³⁷, 16432, F₂, 33) (dual of [16432, 16195, 34]-code), using
    - constructionÂ X applied to C_e(32) âŠ‚ C_e(26) [i] based on
      1. linear OA(2²²⁵, 16384, F₂, 33) (dual of [16384, 16159, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      2. 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]
      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(2²³⁶, 2053, F₂, 40, 32) (dual of [(2053, 40), 81884, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row