MinT - Information on Result #1444398

Information on Result #1444398

Linear OOA(8⁹⁰, 31489, F₈, 2, 20) (dual of [(31489, 2), 62888, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(8⁹⁰, 31489, F₈, 20) (dual of [31489, 31399, 21]-code), using

discarding factors / shortening the dual code based on linear OA(8⁹⁰, 32787, F₈, 20) (dual of [32787, 32697, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8⁸⁹, 32786, F₈, 20) (dual of [32786, 32697, 21]-code), using
  - constructionÂ X applied to C_e(19) âŠ‚ C_e(16) [i] based on
    1. linear OA(8⁸⁶, 32768, F₈, 20) (dual of [32768, 32682, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    2. linear OA(8⁷¹, 32768, F₈, 17) (dual of [32768, 32697, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(8³, 18, F₈, 2) (dual of [18, 15, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(8³, 63, F₈, 2) (dual of [63, 60, 3]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 8²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]

Mode: 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(8⁹⁰, 15744, F₈, 3, 20) (dual of [(15744, 3), 47142, 21]-NRT-code)	[i]		OOA Folding