MinT - Information on Result #1589032

Information on Result #1589032

Linear OOA(2⁶², 9283, F₂, 4, 9) (dual of [(9283, 4), 37070, 10]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁶², 9283, F₂, 3, 9) (dual of [(9283, 3), 27787, 10]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁶², 10928, F₂, 3, 9) (dual of [(10928, 3), 32722, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2⁶², 32784, F₂, 9) (dual of [32784, 32722, 10]-code), using
  - constructionÂ X applied to C_e(8) âŠ‚ C_e(6) [i] based on
    1. linear OA(2⁶¹, 32768, F₂, 9) (dual of [32768, 32707, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    2. linear OA(2⁴⁶, 32768, F₂, 7) (dual of [32768, 32722, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. 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(2⁶², 9282, F₂, 5, 9) (dual of [(9282, 5), 46348, 10]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2⁶², 9282, F₂, 6, 9) (dual of [(9282, 6), 55630, 10]-NRT-code)	[i]
3	Linear OOA(2⁶², 9282, F₂, 7, 9) (dual of [(9282, 7), 64912, 10]-NRT-code)	[i]
4	Linear OOA(2⁶², 9282, F₂, 8, 9) (dual of [(9282, 8), 74194, 10]-NRT-code)	[i]