MinT - Information on Result #1518822

Information on Result #1518822

Linear OOA(2²⁴⁵, 1485, F₂, 3, 39) (dual of [(1485, 3), 4210, 40]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴⁵, 1485, F₂, 2, 39) (dual of [(1485, 2), 2725, 40]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴⁵, 2074, F₂, 2, 39) (dual of [(2074, 2), 3903, 40]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(2²⁴¹, 2072, F₂, 2, 39) (dual of [(2072, 2), 3903, 40]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2²⁴¹, 4144, F₂, 39) (dual of [4144, 3903, 40]-code), using
    - constructionÂ X applied to C_e(38) âŠ‚ C_e(32) [i] based on
      1. linear OA(2²²⁹, 4096, F₂, 39) (dual of [4096, 3867, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
      2. linear OA(2¹⁹³, 4096, F₂, 33) (dual of [4096, 3903, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [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(2²⁴⁵, 742, F₂, 6, 39) (dual of [(742, 6), 4207, 40]-NRT-code)	[i]		OOA Folding