MinT - Information on Result #1490120

Information on Result #1490120

Linear OOA(8¹⁰⁵, 2545, F₈, 3, 28) (dual of [(2545, 3), 7530, 29]-NRT-code), using OOA 2-folding based on linear OOA(8¹⁰⁵, 5090, F₈, 2, 28) (dual of [(5090, 2), 10075, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(8¹⁰⁵, 5091, F₈, 2, 28) (dual of [(5091, 2), 10077, 29]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8¹⁰⁵, 5091, F₈, 28) (dual of [5091, 4986, 29]-code), using
  - 983 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 0, 0, 0, 1, 12 times 0, 1, 36 times 0, 1, 90 times 0, 1, 187 times 0, 1, 290 times 0, 1, 358 times 0) [i] based on linear OA(8⁹⁷, 4100, F₈, 28) (dual of [4100, 4003, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(26) [i] based on
      1. linear OA(8⁹⁷, 4096, F₈, 28) (dual of [4096, 3999, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 8⁴âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(8⁹³, 4096, F₈, 27) (dual of [4096, 4003, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 8⁴âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      3. linear OA(8⁰, 4, F₈, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.