MinT - Information on Result #1648385

Information on Result #1648385

Linear OOA(3²⁰³, 151851, F₃, 5, 25) (dual of [(151851, 5), 759052, 26]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁰³, 151851, F₃, 3, 25) (dual of [(151851, 3), 455350, 26]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁰³, 177162, F₃, 3, 25) (dual of [(177162, 3), 531283, 26]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²⁰², 177162, F₃, 3, 25) (dual of [(177162, 3), 531284, 26]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²⁰², 531486, F₃, 25) (dual of [531486, 531284, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(19) [i] based on
      1. linear OA(3¹⁹³, 531441, F₃, 25) (dual of [531441, 531248, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(3¹⁵⁷, 531441, F₃, 20) (dual of [531441, 531284, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      3. linear OA(3⁹, 45, F₃, 4) (dual of [45, 36, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁹, 80, F₃, 4) (dual of [80, 71, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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.