MinT - Information on Result #1635453

Information on Result #1635453

Linear OOA(2¹⁹⁴, 3571, F₂, 5, 27) (dual of [(3571, 5), 17661, 28]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁹⁴, 3571, F₂, 4, 27) (dual of [(3571, 4), 14090, 28]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁹⁴, 4105, F₂, 4, 27) (dual of [(4105, 4), 16226, 28]-NRT-code), using
- 2³ times duplication [i] based on linear OOA(2¹⁹¹, 4105, F₂, 4, 27) (dual of [(4105, 4), 16229, 28]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹⁹¹, 16420, F₂, 27) (dual of [16420, 16229, 28]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(2¹⁹⁰, 16419, F₂, 27) (dual of [16419, 16229, 28]-code), using
      - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
        linear OA(2¹⁸³, 16384, F₂, 27) (dual of [16384, 16201, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        linear OA(2¹⁵⁵, 16384, F₂, 23) (dual of [16384, 16229, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(2⁷, 35, F₂, 3) (dual of [35, 28, 4]-code or 35-cap in PG(6,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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

None.