MinT - Information on Result #1484765

Information on Result #1484765

Linear OOA(5⁶¹, 195327, F₅, 3, 9) (dual of [(195327, 3), 585920, 10]-NRT-code), using OOA 2-folding based on linear OOA(5⁶¹, 390654, F₅, 2, 9) (dual of [(390654, 2), 781247, 10]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5⁶¹, 390654, F₅, 9) (dual of [390654, 390593, 10]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(5⁶⁰, 390652, F₅, 9) (dual of [390652, 390592, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(5) [i] based on
      1. linear OA(5⁵⁷, 390625, F₅, 9) (dual of [390625, 390568, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(5³³, 390625, F₅, 6) (dual of [390625, 390592, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 390624Â = 5⁸âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      3. linear OA(5³, 27, F₅, 2) (dual of [27, 24, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(5³, 31, F₅, 2) (dual of [31, 28, 3]-code), using
        Hamming code H(3,5) [i]
  2. linear OA(5⁶⁰, 390653, F₅, 8) (dual of [390653, 390593, 9]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 5⁶⁰Â > V_b^sâˆ’1(kâˆ’1)Â = 4513 343280 562703 886476 626708 811594 606225 [i]
  3. linear OA(5⁰, 1, F₅, 0) (dual of [1, 1, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 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.