MinT - Information on Result #1589449

Information on Result #1589449

Linear OOA(2⁸¹, 654, F₂, 4, 15) (dual of [(654, 4), 2535, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁸¹, 654, F₂, 3, 15) (dual of [(654, 3), 1881, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁸¹, 687, F₂, 3, 15) (dual of [(687, 3), 1980, 16]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2⁸⁰, 687, F₂, 3, 15) (dual of [(687, 3), 1981, 16]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁸⁰, 2061, F₂, 15) (dual of [2061, 1981, 16]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(2⁷⁹, 2060, F₂, 15) (dual of [2060, 1981, 16]-code), using
      - constructionÂ X applied to C_e(14) âŠ‚ C_e(12) [i] based on
        linear OA(2⁷⁸, 2048, F₂, 15) (dual of [2048, 1970, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(2⁶⁷, 2048, F₂, 13) (dual of [2048, 1981, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(2¹, 12, F₂, 1) (dual of [12, 11, 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(2⁸¹, 327, F₂, 7, 15) (dual of [(327, 7), 2208, 16]-NRT-code)	[i]		OOA Folding