MinT - Information on Result #2251845

Information on Result #2251845

Linear OA(8¹⁶⁷, 2097234, F₈, 24) (dual of [2097234, 2097067, 25]-code), using 1 times truncation based on linear OA(8¹⁶⁸, 2097235, F₈, 25) (dual of [2097235, 2097067, 26]-code), using

constructionÂ X applied to C_e(24) âŠ‚ C_e(13) [i] based on
1. linear OA(8¹⁴⁸, 2097152, F₈, 25) (dual of [2097152, 2097004, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
2. linear OA(8⁸⁵, 2097152, F₈, 14) (dual of [2097152, 2097067, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
3. linear OA(8²⁰, 83, F₈, 10) (dual of [83, 63, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(8²⁰, 130, F₈, 10) (dual of [130, 110, 11]-code), using
    - trace code [i] based on linear OA(64¹⁰, 65, F₆₄, 10) (dual of [65, 55, 11]-code or 65-arc in PG(9,64)), using
      - extended Reedâ€“Solomon code RS_e(55,64) [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(8¹⁶⁷, 1048617, F₈, 2, 24) (dual of [(1048617, 2), 2097067, 25]-NRT-code)	[i]		OOA Folding
2	Linear OOA(8¹⁶⁷, 699078, F₈, 3, 24) (dual of [(699078, 3), 2097067, 25]-NRT-code)	[i]		OOA Folding