MinT - Information on Result #1484901

Information on Result #1484901

Linear OOA(5⁵⁴, 1427, F₅, 3, 13) (dual of [(1427, 3), 4227, 14]-NRT-code), using OOA 2-folding based on linear OOA(5⁵⁴, 2854, F₅, 2, 13) (dual of [(2854, 2), 5654, 14]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(5⁵⁴, 2855, F₅, 2, 13) (dual of [(2855, 2), 5656, 14]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5⁵⁴, 2855, F₅, 13) (dual of [2855, 2801, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(5⁵⁴, 3139, F₅, 13) (dual of [3139, 3085, 14]-code), using
    - 2 times code embedding in larger space [i] based on linear OA(5⁵², 3137, F₅, 13) (dual of [3137, 3085, 14]-code), using
      - constructionÂ X applied to C([0,6]) âŠ‚ C([0,5]) [i] based on
        linear OA(5⁵¹, 3126, F₅, 13) (dual of [3126, 3075, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126Â | 5¹⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
        linear OA(5⁴¹, 3126, F₅, 11) (dual of [3126, 3085, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126Â | 5¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
        linear OA(5¹, 11, F₅, 1) (dual of [11, 10, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 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.