MinT - Information on Result #1620602

Information on Result #1620602

Linear OOA(3⁵⁰, 1576, F₃, 5, 10) (dual of [(1576, 5), 7830, 11]-NRT-code), using OOA 2-folding based on linear OOA(3⁵⁰, 3152, F₃, 3, 10) (dual of [(3152, 3), 9406, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁵⁰, 3153, F₃, 3, 10) (dual of [(3153, 3), 9409, 11]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁵⁰, 3153, F₃, 2, 10) (dual of [(3153, 2), 6256, 11]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁵⁰, 3285, F₃, 2, 10) (dual of [(3285, 2), 6520, 11]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3⁵⁰, 6570, F₃, 10) (dual of [6570, 6520, 11]-code), using
      - constructionÂ X applied to C_e(9) âŠ‚ C_e(7) [i] based on
        linear OA(3⁴⁹, 6561, F₃, 10) (dual of [6561, 6512, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(3⁴¹, 6561, F₃, 8) (dual of [6561, 6520, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(3¹, 9, F₃, 1) (dual of [9, 8, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.