MinT - Information on Result #1595700

Information on Result #1595700

Linear OOA(2²⁰⁵, 1381, F₂, 4, 33) (dual of [(1381, 4), 5319, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁰⁵, 1381, F₂, 3, 33) (dual of [(1381, 3), 3938, 34]-NRT-code), using

OOA 3-folding [i] based on linear OA(2²⁰⁵, 4143, F₂, 33) (dual of [4143, 3938, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2²⁰⁵, 4144, F₂, 33) (dual of [4144, 3939, 34]-code), using
  - constructionÂ X applied to C_e(32) âŠ‚ C_e(26) [i] based on
    1. 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]
    2. linear OA(2¹⁵⁷, 4096, F₂, 27) (dual of [4096, 3939, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’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(2²⁰⁶, 1381, F₂, 4, 33) (dual of [(1381, 4), 5318, 34]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2²⁰⁵, 690, F₂, 7, 33) (dual of [(690, 7), 4625, 34]-NRT-code)	[i]		OOA Folding
3	Linear OOA(2²⁰⁵, 690, F₂, 8, 33) (dual of [(690, 8), 5315, 34]-NRT-code)	[i]		OOA Folding