MinT - Information on Result #1685974

Information on Result #1685974

Linear OOA(2²¹², 6124, F₂, 7, 28) (dual of [(6124, 7), 42656, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹², 6124, F₂, 5, 28) (dual of [(6124, 5), 30408, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²¹², 6556, F₂, 5, 28) (dual of [(6556, 5), 32568, 29]-NRT-code), using
- strength reduction [i] based on linear OOA(2²¹², 6556, F₂, 5, 29) (dual of [(6556, 5), 32568, 30]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(2²¹², 32780, F₂, 29) (dual of [32780, 32568, 30]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²¹², 32784, F₂, 29) (dual of [32784, 32572, 30]-code), using
      - constructionÂ X applied to C_e(28) âŠ‚ C_e(26) [i] based on
        linear OA(2²¹¹, 32768, F₂, 29) (dual of [32768, 32557, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(2¹⁹⁶, 32768, F₂, 27) (dual of [32768, 32572, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        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(2²¹², 3061, F₂, 35, 28) (dual of [(3061, 35), 106923, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row