MinT - Information on Result #1443545

Information on Result #1443545

Linear OOA(8⁵⁷, 246531, F₈, 2, 11) (dual of [(246531, 2), 493005, 12]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(8⁵⁷, 246531, F₈, 11) (dual of [246531, 246474, 12]-code), using

discarding factors / shortening the dual code based on linear OA(8⁵⁷, 262159, F₈, 11) (dual of [262159, 262102, 12]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8⁵⁶, 262158, F₈, 11) (dual of [262158, 262102, 12]-code), using
  - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
    1. linear OA(8⁵⁵, 262144, F₈, 11) (dual of [262144, 262089, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    2. linear OA(8⁴³, 262144, F₈, 9) (dual of [262144, 262101, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    3. linear OA(8¹³, 14, F₈, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,8)), using
      - dual of repetition code with length 14 [i]
    4. linear OA(8¹, 14, F₈, 1) (dual of [14, 13, 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: 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(8⁵⁷, 123265, F₈, 3, 11) (dual of [(123265, 3), 369738, 12]-NRT-code)	[i]		OOA Folding