MinT - Information on Result #1513779

Information on Result #1513779

Linear OOA(2¹⁷⁷, 724, F₂, 3, 32) (dual of [(724, 3), 1995, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁷⁷, 724, F₂, 2, 32) (dual of [(724, 2), 1271, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁷⁷, 1029, F₂, 2, 32) (dual of [(1029, 2), 1881, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁷⁷, 2058, F₂, 32) (dual of [2058, 1881, 33]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁷⁷, 2059, F₂, 32) (dual of [2059, 1882, 33]-code), using
    - 1 times truncation [i] based on linear OA(2¹⁷⁸, 2060, F₂, 33) (dual of [2060, 1882, 34]-code), using
      - constructionÂ X applied to C_e(32) âŠ‚ C_e(30) [i] based on
        linear OA(2¹⁷⁷, 2048, F₂, 33) (dual of [2048, 1871, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
        linear OA(2¹⁶⁶, 2048, F₂, 31) (dual of [2048, 1882, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [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(2¹⁷⁷, 362, F₂, 6, 32) (dual of [(362, 6), 1995, 33]-NRT-code)	[i]		OOA Folding