MinT - Information on Result #1589450

Information on Result #1589450

Linear OOA(2⁸¹, 697, F₂, 4, 14) (dual of [(697, 4), 2707, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁸¹, 697, F₂, 2, 14) (dual of [(697, 2), 1313, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁸¹, 1031, F₂, 2, 14) (dual of [(1031, 2), 1981, 15]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2⁷⁹, 1030, F₂, 2, 14) (dual of [(1030, 2), 1981, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2⁷⁹, 2060, F₂, 14) (dual of [2060, 1981, 15]-code), using
    - strength reduction [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, 348, F₂, 7, 14) (dual of [(348, 7), 2355, 15]-NRT-code)	[i]		OOA Folding