MinT - Information on Result #1685975

Information on Result #1685975

Linear OOA(2²¹², 10440, F₂, 7, 27) (dual of [(10440, 7), 72868, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹², 10440, F₂, 6, 27) (dual of [(10440, 6), 62428, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²¹², 10925, F₂, 6, 27) (dual of [(10925, 6), 65338, 28]-NRT-code), using
- 2² times duplication [i] based on linear OOA(2²¹⁰, 10925, F₂, 6, 27) (dual of [(10925, 6), 65340, 28]-NRT-code), using
  - OOA 6-folding [i] based on linear OA(2²¹⁰, 65550, F₂, 27) (dual of [65550, 65340, 28]-code), using
    - discarding factors / shortening the dual code based on linear OA(2²¹⁰, 65553, F₂, 27) (dual of [65553, 65343, 28]-code), using
      - constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
        linear OA(2²⁰⁹, 65536, F₂, 27) (dual of [65536, 65327, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        linear OA(2¹⁹³, 65536, F₂, 25) (dual of [65536, 65343, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
        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(2²¹², 5219, F₂, 35, 27) (dual of [(5219, 35), 182453, 28]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row