MinT - Information on Result #1590906

Information on Result #1590906

Linear OOA(2¹²⁶, 1057, F₂, 4, 21) (dual of [(1057, 4), 4102, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹²⁶, 1057, F₂, 3, 21) (dual of [(1057, 3), 3045, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹²⁶, 1371, F₂, 3, 21) (dual of [(1371, 3), 3987, 22]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹²³, 1370, F₂, 3, 21) (dual of [(1370, 3), 3987, 22]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2¹²³, 4110, F₂, 21) (dual of [4110, 3987, 22]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(2¹²², 4109, F₂, 21) (dual of [4109, 3987, 22]-code), using
      - constructionÂ X applied to C_e(20) âŠ‚ C_e(18) [i] based on
        linear OA(2¹²¹, 4096, F₂, 21) (dual of [4096, 3975, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(2¹⁰⁹, 4096, F₂, 19) (dual of [4096, 3987, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(2¹²⁶, 528, F₂, 8, 21) (dual of [(528, 8), 4098, 22]-NRT-code)	[i]		OOA Folding