MinT - Information on Result #1449653

Information on Result #1449653

Linear OOA(9⁶⁹, 486265, F₉, 2, 13) (dual of [(486265, 2), 972461, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(9⁶⁹, 486265, F₉, 13) (dual of [486265, 486196, 14]-code), using

discarding factors / shortening the dual code based on linear OA(9⁶⁹, 531456, F₉, 13) (dual of [531456, 531387, 14]-code), using
- 1 times code embedding in larger space [i] based on linear OA(9⁶⁸, 531455, F₉, 13) (dual of [531455, 531387, 14]-code), using
  - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
    1. linear OA(9⁶⁷, 531441, F₉, 13) (dual of [531441, 531374, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 9⁶âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(9⁵⁵, 531441, F₉, 11) (dual of [531441, 531386, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 9⁶âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
    3. linear OA(9¹³, 14, F₉, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,9)), using
      - dual of repetition code with length 14 [i]
    4. linear OA(9¹, 14, F₉, 1) (dual of [14, 13, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(9¹, 728, F₉, 1) (dual of [728, 727, 2]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 9³âˆ’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(9⁶⁹, 243132, F₉, 3, 13) (dual of [(243132, 3), 729327, 14]-NRT-code)	[i]		OOA Folding