MinT - Information on Result #1629878

Information on Result #1629878

Linear OOA(2⁶¹, 10928, F₂, 5, 8) (dual of [(10928, 5), 54579, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁶¹, 10928, F₂, 3, 8) (dual of [(10928, 3), 32723, 9]-NRT-code), using

OOA 3-folding [i] based on linear OA(2⁶¹, 32784, F₂, 8) (dual of [32784, 32723, 9]-code), using
- 1 times truncation [i] based on linear OA(2⁶², 32785, F₂, 9) (dual of [32785, 32723, 10]-code), using
  - constructionÂ X4 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(2¹⁶, 17, F₂, 15) (dual of [17, 1, 16]-code), using
      - strength reduction [i] based on linear OA(2¹⁶, 17, F₂, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
        dual of repetition code with length 17 [i]
    4. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 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, 10928, F₂, 5, 8) (dual of [(10928, 5), 54578, 9]-NRT-code)	[i]		OOA Duplication