MinT - Information on Result #1701680

Information on Result #1701680

Linear OOA(2¹⁹², 74901, F₂, 8, 21) (dual of [(74901, 8), 599016, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹², 74901, F₂, 7, 21) (dual of [(74901, 7), 524115, 22]-NRT-code), using

OOA 7-folding [i] based on linear OA(2¹⁹², 524307, F₂, 21) (dual of [524307, 524115, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁹², 524308, F₂, 21) (dual of [524308, 524116, 22]-code), using
  - constructionÂ X applied to C_e(20) âŠ‚ C_e(18) [i] based on
    1. linear OA(2¹⁹¹, 524288, F₂, 21) (dual of [524288, 524097, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    2. linear OA(2¹⁷², 524288, F₂, 19) (dual of [524288, 524116, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(2¹, 20, F₂, 1) (dual of [20, 19, 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(2¹⁹³, 74901, F₂, 8, 21) (dual of [(74901, 8), 599015, 22]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁹⁴, 74901, F₂, 8, 21) (dual of [(74901, 8), 599014, 22]-NRT-code)	[i]
3	Linear OOA(2¹⁹⁵, 74901, F₂, 8, 21) (dual of [(74901, 8), 599013, 22]-NRT-code)	[i]
4	Linear OOA(2¹⁹⁶, 74901, F₂, 8, 21) (dual of [(74901, 8), 599012, 22]-NRT-code)	[i]