MinT - Information on Result #1595867

Information on Result #1595867

Linear OOA(2²⁰⁷, 1299, F₂, 4, 34) (dual of [(1299, 4), 4989, 35]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁰⁷, 1299, F₂, 3, 34) (dual of [(1299, 3), 3690, 35]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁰⁷, 1370, F₂, 3, 34) (dual of [(1370, 3), 3903, 35]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2²⁰⁷, 4110, F₂, 34) (dual of [4110, 3903, 35]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2²⁰⁵, 4108, F₂, 34) (dual of [4108, 3903, 35]-code), using
    - 1 times truncation [i] based on linear OA(2²⁰⁶, 4109, F₂, 35) (dual of [4109, 3903, 36]-code), using
      - constructionÂ X applied to C_e(34) âŠ‚ C_e(32) [i] based on
        linear OA(2²⁰⁵, 4096, F₂, 35) (dual of [4096, 3891, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
        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]
        linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(2²⁰⁷, 649, F₂, 7, 34) (dual of [(649, 7), 4336, 35]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁰⁷, 649, F₂, 8, 34) (dual of [(649, 8), 4985, 35]-NRT-code)	[i]		OOA Folding