MinT - Information on Result #1706120

Information on Result #1706120

Linear OOA(2²⁴⁸, 74901, F₂, 8, 26) (dual of [(74901, 8), 598960, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁴⁸, 74901, F₂, 7, 26) (dual of [(74901, 7), 524059, 27]-NRT-code), using

OOA 7-folding [i] based on linear OA(2²⁴⁸, 524307, F₂, 26) (dual of [524307, 524059, 27]-code), using
- 1 times truncation [i] based on linear OA(2²⁴⁹, 524308, F₂, 27) (dual of [524308, 524059, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
    1. linear OA(2²⁴⁸, 524288, F₂, 27) (dual of [524288, 524040, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(2²²⁹, 524288, F₂, 25) (dual of [524288, 524059, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(2²⁴⁹, 74901, F₂, 8, 26) (dual of [(74901, 8), 598959, 27]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2²⁵⁰, 74901, F₂, 8, 26) (dual of [(74901, 8), 598958, 27]-NRT-code)	[i]
3	Linear OOA(2²⁵¹, 74901, F₂, 8, 26) (dual of [(74901, 8), 598957, 27]-NRT-code)	[i]
4	Linear OOA(2²⁵², 74901, F₂, 8, 26) (dual of [(74901, 8), 598956, 27]-NRT-code)	[i]