MinT - Information on Result #2306253

Information on Result #2306253

Linear OA(2²³³, 281, F₂, 87) (dual of [281, 48, 88]-code), using 3 times code embedding in larger space based on linear OA(2²³⁰, 278, F₂, 87) (dual of [278, 48, 88]-code), using

adding a parity check bit [i] based on linear OA(2²²⁹, 277, F₂, 86) (dual of [277, 48, 87]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(2²¹¹, 258, F₂, 86) (dual of [258, 47, 87]-code), using
    - 1 times truncation [i] based on linear OA(2²¹², 259, F₂, 87) (dual of [259, 47, 88]-code), using
      - constructionÂ X applied to C_e(86) âŠ‚ C_e(84) [i] based on
        linear OA(2²¹¹, 256, F₂, 87) (dual of [256, 45, 88]-code), using an extension C_e(86) of the primitive narrow-sense BCH-code C(I) with length 255Â = 2⁸âˆ’1, defining interval IÂ =Â [1,86], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 87 [i]
        linear OA(2²⁰⁹, 256, F₂, 85) (dual of [256, 47, 86]-code), using an extension C_e(84) of the primitive narrow-sense BCH-code C(I) with length 255Â = 2⁸âˆ’1, defining interval IÂ =Â [1,84], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 85 [i]
        linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 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]
  2. linear OA(2²¹¹, 259, F₂, 68) (dual of [259, 48, 69]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 2²¹¹Â > V_b^sâˆ’1(kâˆ’1)Â = 1288 439491 289880 083651 028009 614516 457982 306386 781906 313688 090836 [i]
  3. linear OA(2¹⁷, 18, F₂, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
    - dual of repetition code with length 18 [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.