MinT - Information on Result #944699

Information on Result #944699

Linear OOA(8²⁸, 262155, F₈, 3, 5) (dual of [(262155, 3), 786437, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(8²⁸, 262156, F₈, 2, 5) (dual of [(262156, 2), 524284, 6]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(8², 9, F₈, 2, 2) (dual of [(9, 2), 16, 3]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;16,8) [i]
2. linear OOA(8²⁶, 262147, F₈, 2, 5) (dual of [(262147, 2), 524268, 6]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(8²⁶, 524294, F₈, 5) (dual of [524294, 524268, 6]-code), using
    - trace code [i] based on linear OA(64¹³, 262147, F₆₄, 5) (dual of [262147, 262134, 6]-code), using
      - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(64¹³, 262144, F₆₄, 5) (dual of [262144, 262131, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(64¹⁰, 262144, F₆₄, 4) (dual of [262144, 262134, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁰², 5854557, F₈, 3, 10) (dual of [(5854557, 3), 17563569, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(8¹¹⁰, 5854557, F₈, 3, 11) (dual of [(5854557, 3), 17563561, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs