MinT - Information on Result #895489

Information on Result #895489

Linear OOA(4¹¹⁷, 4196353, F₄, 2, 11) (dual of [(4196353, 2), 8392589, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4²⁰, 2052, F₄, 2, 5) (dual of [(2052, 2), 4084, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4²⁰, 4104, F₄, 5) (dual of [4104, 4084, 6]-code), using
  - constructionÂ X4 applied to C_e(4) âŠ‚ C_e(2) [i] based on
    1. linear OA(4¹⁹, 4096, F₄, 5) (dual of [4096, 4077, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    2. linear OA(4¹³, 4096, F₄, 3) (dual of [4096, 4083, 4]-code or 4096-cap in PG(12,4)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
    3. linear OA(4⁷, 8, F₄, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,4)), using
      - dual of repetition code with length 8 [i]
    4. linear OA(4¹, 8, F₄, 1) (dual of [8, 7, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OOA(4⁹⁷, 4194301, F₄, 2, 11) (dual of [(4194301, 2), 8388505, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4⁹⁷, 8388602, F₄, 11) (dual of [8388602, 8388505, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁹⁷, large, F₄, 11) (dual of [large, large−97, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.