MinT - Information on Result #1509247

Information on Result #1509247

Linear OOA(2⁴⁶, 254, F₂, 3, 10) (dual of [(254, 3), 716, 11]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁴⁶, 254, F₂, 2, 10) (dual of [(254, 2), 462, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁴⁶, 260, F₂, 2, 10) (dual of [(260, 2), 474, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2⁴⁶, 520, F₂, 10) (dual of [520, 474, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁴⁶, 521, F₂, 10) (dual of [521, 475, 11]-code), using
    - 1 times truncation [i] based on linear OA(2⁴⁷, 522, F₂, 11) (dual of [522, 475, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(8) [i] based on
        linear OA(2⁴⁶, 512, F₂, 11) (dual of [512, 466, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(2³⁷, 512, F₂, 9) (dual of [512, 475, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2¹, 10, F₂, 1) (dual of [10, 9, 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(2⁴⁶, 127, F₂, 5, 10) (dual of [(127, 5), 589, 11]-NRT-code)	[i]		OOA Folding