MinT - Information on Result #1705673

Information on Result #1705673

Linear OOA(2²⁴³, 5972, F₂, 8, 32) (dual of [(5972, 8), 47533, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴³, 5972, F₂, 5, 32) (dual of [(5972, 5), 29617, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴³, 6557, F₂, 5, 32) (dual of [(6557, 5), 32542, 33]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2²⁴³, 32785, F₂, 32) (dual of [32785, 32542, 33]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2²⁴¹, 32783, F₂, 32) (dual of [32783, 32542, 33]-code), using
    - 1 times truncation [i] based on linear OA(2²⁴², 32784, F₂, 33) (dual of [32784, 32542, 34]-code), using
      - constructionÂ X applied to C_e(32) âŠ‚ C_e(30) [i] based on
        linear OA(2²⁴¹, 32768, F₂, 33) (dual of [32768, 32527, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
        linear OA(2²²⁶, 32768, F₂, 31) (dual of [32768, 32542, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
        linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 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(2²⁴³, 2985, F₂, 40, 32) (dual of [(2985, 40), 119157, 33]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row