MinT - Information on Result #895701

Information on Result #895701

Linear OOA(4²²⁹, 4196360, F₄, 2, 21) (dual of [(4196360, 2), 8392491, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁴⁸, 2059, F₄, 2, 10) (dual of [(2059, 2), 4070, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4⁴⁸, 4118, F₄, 10) (dual of [4118, 4070, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁴⁸, 4119, F₄, 10) (dual of [4119, 4071, 11]-code), using
    - constructionÂ X applied to C_e(9) âŠ‚ C_e(5) [i] based on
      1. linear OA(4⁴³, 4096, F₄, 10) (dual of [4096, 4053, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      2. linear OA(4²⁵, 4096, F₄, 6) (dual of [4096, 4071, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 4⁶âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      3. linear OA(4⁵, 23, F₄, 3) (dual of [23, 18, 4]-code or 23-cap in PG(4,4)), using
        discarding factors / shortening the dual code based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [i]
linear OOA(4¹⁸¹, 4194301, F₄, 2, 21) (dual of [(4194301, 2), 8388421, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁸¹, 8388602, F₄, 21) (dual of [8388602, 8388421, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁸¹, large, F₄, 21) (dual of [large, large−181, 22]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [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.