MinT - Information on Result #1011882

Information on Result #1011882

Linear OOA(4¹²⁶, 2796287, F₄, 3, 13) (dual of [(2796287, 3), 8388735, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4¹⁷, 86, F₄, 3, 6) (dual of [(86, 3), 241, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4¹⁷, 258, F₄, 6) (dual of [258, 241, 7]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁷, 260, F₄, 6) (dual of [260, 243, 7]-code), using
    - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
      1. linear OA(4¹⁷, 256, F₄, 6) (dual of [256, 239, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      2. linear OA(4¹³, 256, F₄, 5) (dual of [256, 243, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      3. linear OA(4⁰, 4, F₄, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
linear OOA(4¹⁰⁹, 2796201, F₄, 3, 13) (dual of [(2796201, 3), 8388494, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4¹⁰⁹, large, F₄, 13) (dual of [large, large−109, 14]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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.