MinT - Information on Result #1600966

Information on Result #1600966

Linear OOA(2²⁶⁰, 2207, F₂, 4, 39) (dual of [(2207, 4), 8568, 40]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁶⁰, 2207, F₂, 3, 39) (dual of [(2207, 3), 6361, 40]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁶⁰, 2746, F₂, 3, 39) (dual of [(2746, 3), 7978, 40]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2²⁶⁰, 8238, F₂, 39) (dual of [8238, 7978, 40]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁶⁰, 8240, F₂, 39) (dual of [8240, 7980, 40]-code), using
    - constructionÂ X applied to C_e(38) âŠ‚ C_e(32) [i] based on
      1. linear OA(2²⁴⁸, 8192, F₂, 39) (dual of [8192, 7944, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
      2. linear OA(2²⁰⁹, 8192, F₂, 33) (dual of [8192, 7983, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’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(2²⁶⁰, 1103, F₂, 8, 39) (dual of [(1103, 8), 8564, 40]-NRT-code)	[i]		OOA Folding