MinT - Information on Result #1681288

Information on Result #1681288

Linear OOA(2¹³⁶, 107847, F₂, 7, 14) (dual of [(107847, 7), 754793, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹³⁶, 107847, F₂, 4, 14) (dual of [(107847, 4), 431252, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹³⁶, 131077, F₂, 4, 14) (dual of [(131077, 4), 524172, 15]-NRT-code), using
- 2² times duplication [i] based on linear OOA(2¹³⁴, 131077, F₂, 4, 14) (dual of [(131077, 4), 524174, 15]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹³⁴, 524308, F₂, 14) (dual of [524308, 524174, 15]-code), using
    - 1 times truncation [i] based on linear OA(2¹³⁵, 524309, F₂, 15) (dual of [524309, 524174, 16]-code), using
      - constructionÂ X4 applied to C_e(14) âŠ‚ C_e(12) [i] based on
        linear OA(2¹³⁴, 524288, F₂, 15) (dual of [524288, 524154, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(2¹¹⁵, 524288, F₂, 13) (dual of [524288, 524173, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(2²⁰, 21, F₂, 19) (dual of [21, 1, 20]-code), using
        strength reduction [i] based on linear OA(2²⁰, 21, F₂, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
        dual of repetition code with length 21 [i]
        linear OA(2¹, 21, F₂, 1) (dual of [21, 20, 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(2¹³⁶, 107846, F₂, 8, 14) (dual of [(107846, 8), 862632, 15]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹³⁶, 107846, F₂, 21, 14) (dual of [(107846, 21), 2264630, 15]-NRT-code)	[i]		OOA Stacking with Additional Row