MinT - Information on Result #1014531

Information on Result #1014531

Linear OOA(8¹³⁷, 5603326, F₈, 3, 14) (dual of [(5603326, 3), 16809841, 15]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8³¹, 10924, F₈, 3, 7) (dual of [(10924, 3), 32741, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8³¹, 32772, F₈, 7) (dual of [32772, 32741, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(8³¹, 32773, F₈, 7) (dual of [32773, 32742, 8]-code), using
    - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
      1. linear OA(8³¹, 32768, F₈, 7) (dual of [32768, 32737, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OA(8²⁶, 32768, F₈, 6) (dual of [32768, 32742, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      3. linear OA(8⁰, 5, F₈, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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(8¹⁰⁶, 5592402, F₈, 3, 14) (dual of [(5592402, 3), 16777100, 15]-NRT-code), using
- trace code [i] based on linear OOA(64⁵³, 2796201, F₆₄, 3, 14) (dual of [(2796201, 3), 8388550, 15]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64⁵³, large, F₆₄, 14) (dual of [large, large−53, 15]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.