MinT - Information on Result #978842

Information on Result #978842

Linear OOA(8³⁸, 10927, F₈, 3, 8) (dual of [(10927, 3), 32743, 9]-NRT-code), using OOA 3-folding based on linear OA(8³⁸, 32781, F₈, 8) (dual of [32781, 32743, 9]-code), using

1 times code embedding in larger space [i] based on linear OA(8³⁷, 32780, F₈, 8) (dual of [32780, 32743, 9]-code), using
- constructionÂ X4 applied to C_e(8) âŠ‚ C_e(5) [i] based on
  1. linear OA(8³⁶, 32768, F₈, 9) (dual of [32768, 32732, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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(8¹¹, 12, F₈, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,8)), using
    - dual of repetition code with length 12 [i]
  4. linear OA(8¹, 12, F₈, 1) (dual of [12, 11, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹, 511, F₈, 1) (dual of [511, 510, 2]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 511Â = 8³âˆ’1, defining interval IÂ =Â [0,0], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [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(8¹⁶⁰, 5603329, F₈, 3, 16) (dual of [(5603329, 3), 16809827, 17]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(8¹⁶⁸, 5603329, F₈, 3, 17) (dual of [(5603329, 3), 16809819, 18]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs