Tabulate results of using the GUAVA (GAP package) commands CyclicCodes(n,GF(2)); MinimumDistance(C); CoveringRadius(C); The numbering is that GUAVA's ordering of CyclicCodes(n,GF(2)), which is presumably dependent on how the polynomial factors of x^35-1 get ordered. 11-2004,wdj@usna.edu +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C: a cyclic [35,35,1]0 enumerated code over GF(2) Covering radius: 0 number 1 out of 64 C: a cyclic [35,34,2]1 enumerated code over GF(2) Covering radius: 1 number 2 out of 64 C: a cyclic [35,32,2]1 enumerated code over GF(2) Covering radius: 1 number 34 out of 64 C: a cyclic [35,32,2]1 enumerated code over GF(2) Covering radius: 1 number 50 out of 64 C: a cyclic [35,31,2]2 enumerated code over GF(2) Covering radius: 2 number 58 out of 64 C: a cyclic [35,31,2]3 enumerated code over GF(2) Covering radius: 3 number 3 out of 64 C: a cyclic [35,31,2]3 enumerated code over GF(2) Covering radius: 3 number 19 out of 64 C: a cyclic [35,30,2]5 enumerated code over GF(2) Covering radius: 5 number 27 out of 64 C: a cyclic [35,29,2]3 enumerated code over GF(2) Covering radius: 3 number 35 out of 64 C: a cyclic [35,28,4]3 enumerated code over GF(2) Covering radius: 3 number 51 out of 64 C: a cyclic [35,28,2]7 enumerated code over GF(2) Covering radius: 7 number 4 out of 64 C: a cyclic [35,28,4]3 enumerated code over GF(2) Covering radius: 3 number 43 out of 64 C: a cyclic [35,27,4]5 enumerated code over GF(2) Covering radius: 5 number 12 out of 64 C: a cyclic [35,27,4]5 enumerated code over GF(2) Covering radius: 5 number 20 out of 64 C: a cyclic [35,25,4]5 enumerated code over GF(2) Covering radius: 5 number 36 out of 64 C: a cyclic [35,24,4]7 enumerated code over GF(2) Covering radius: 7 number 5 out of 64 C: a cyclic [35,23,3]4 enumerated code over GF(2) Covering radius: 4 number 62 out of 64 C: a cyclic [35,23,3]4 enumerated code over GF(2) Covering radius: 4 number 64 out of 64 C: a cyclic [35,22,4]5 enumerated code over GF(2) Covering radius: 5 number 31 out of 64 C: a cyclic [35,22,4]5 enumerated code over GF(2) Covering radius: 5 number 33 out of 64 C: a cyclic [35,20,3]5 enumerated code over GF(2) Covering radius: 5 number 47 out of 64 C: a cyclic [35,20,6]5 enumerated code over GF(2) Covering radius: 5 number 49 out of 64 C: a cyclic [35,20,6]5 enumerated code over GF(2) Covering radius: 5 number 55 out of 64 C: a cyclic [35,20,3]5 enumerated code over GF(2) Covering radius: 5 number 57 out of 64 C: a cyclic [35,19,6]7 enumerated code over GF(2) Covering radius: 7 number 24 out of 64 C: a cyclic [35,19,4]6 enumerated code over GF(2) Covering radius: 6 number 26 out of 64 C: a cyclic [35,19,4]6 enumerated code over GF(2) Covering radius: 6 number 16 out of 64 C: a cyclic [35,19,6]7 enumerated code over GF(2) Covering radius: 7 number 18 out of 64 C: a cyclic [35,19,4]6 enumerated code over GF(2) Covering radius: 6 number 59 out of 64 C: a cyclic [35,19,4]6 enumerated code over GF(2) Covering radius: 6 number 61 out of 64 C: a cyclic [35,18,4]8 enumerated code over GF(2) Covering radius: 8 number 28 out of 64 C: a cyclic [35,18,4]8 enumerated code over GF(2) Covering radius: 8 number 30 out of 64 C: a cyclic [35,17,6]7 enumerated code over GF(2) Covering radius: 7 number 42 out of 64 C: a cyclic [35,17,6]7 enumerated code over GF(2) Covering radius: 7 number 40 out of 64 C: a cyclic [35,16,7]7 enumerated code over GF(2) Covering radius: 7 number 46 out of 64 C: a cyclic [35,16,4]7 enumerated code over GF(2) Covering radius: 7 number 44 out of 64 C: a cyclic [35,16,6]8 enumerated code over GF(2) Covering radius: 8 number 9 out of 64 C: a cyclic [35,16,6]8 enumerated code over GF(2) Covering radius: 8 number 11 out of 64 C: a cyclic [35,16,7]7 enumerated code over GF(2) Covering radius: 7 number 52 out of 64 C: a cyclic [35,16,4]7 enumerated code over GF(2) Covering radius: 7 number 54 out of 64 C: a cyclic [35,15,4][ 6 .. 17 ] enumerated code over GF(2) Covering radius: [ 6 .. 17 ] number 13 out of 64 Using IncreaseCoveringRadiusLowerBound(C), got [15..17] C: a cyclic [35,15,8][ 6 .. 15 ] enumerated code over GF(2) Covering radius: [ 6 .. 15 ] number 15 out of 64 Using IncreaseCoveringRadiusLowerBound(C), got [9..17] C: a cyclic [35,15,8][ 6 .. 15 ] enumerated code over GF(2) Covering radius: [ 6 .. 15 ] number 21 out of 64 Using IncreaseCoveringRadiusLowerBound(C), got [9..15] C: a cyclic [35,15,4][ 6 .. 17 ] enumerated code over GF(2) Covering radius: [ 6 .. 17 ] number 23 out of 64 Using IncreaseCoveringRadiusLowerBound(C), got [15..17] C: a cyclic [35,13,8][ 7 .. 15 ] enumerated code over GF(2) Covering radius: [ 7 .. 15 ] number 37 out of 64 Using IncreaseCoveringRadiusLowerBound(C), got [9..15] C: a cyclic [35,13,8][ 7 .. 15 ] enumerated code over GF(2) Covering radius: [ 7 .. 15 ] number 39 out of 64 Using IncreaseCoveringRadiusLowerBound(C), got [9..15] C: a cyclic [35,12,8][ 8 .. 17 ] enumerated code over GF(2) Covering radius: [ 8 .. 17 ] number 6 out of 64 Using IncreaseCoveringRadiusLowerBound(C), got [15..17] C: a cyclic [35,12,8][ 8 .. 17 ] enumerated code over GF(2) Covering radius: [ 8 .. 17 ] number 8 out of 64 Using IncreaseCoveringRadiusLowerBound(C), got [15..17] C: a cyclic [35,11,5][ 8 .. 13 ] enumerated code over GF(2) Covering radius: [ 8 .. 13 ] number 63 out of 64 C: a cyclic [35,10,10][ 9 .. 17 ] enumerated code over GF(2) Covering radius: [ 9 .. 17 ] number 32 out of 64 C: a cyclic [35,8,7][ 10 .. 14 ] enumerated code over GF(2) Covering radius: [ 10 .. 14 ] number 56 out of 64 C: a cyclic [35,8,7][ 10 .. 14 ] enumerated code over GF(2) Covering radius: [ 10 .. 14 ] number 48 out of 64 C: a cyclic [35,7,14][ 11 .. 17 ] enumerated code over GF(2) Covering radius: [ 11 .. 17 ] number 17 out of 64 C: a cyclic [35,7,14][ 11 .. 17 ] enumerated code over GF(2) Covering radius: [ 11 .. 17 ] number 25 out of 64 C: a cyclic [35,7,5][ 11 .. 14 ] enumerated code over GF(2) Covering radius: [ 11 .. 14 ] number 60 out of 64 C: a cyclic [35,6,10][ 11 .. 17 ] enumerated code over GF(2) Covering radius: [ 11 .. 17 ] number 29 out of 64 C: a cyclic [35,5,7]15 enumerated code over GF(2) Covering radius: 15 number 41 out of 64 C: a cyclic [35,4,15][ 15 .. 16 ] enumerated code over GF(2) Covering radius: [ 15 .. 16 ] number 45 out of 64 C: a cyclic [35,4,14][ 15 .. 17 ] enumerated code over GF(2) Covering radius: [ 15 .. 17 ] number 10 out of 64 C: a cyclic [35,4,15][ 15 .. 16 ] enumerated code over GF(2) Covering radius: [ 15 .. 16 ] number 53 out of 64 C: a cyclic [35,3,20][ 16 .. 17 ] enumerated code over GF(2) Covering radius: [ 16 .. 17 ] number 14 out of 64 C: a cyclic [35,3,20][ 16 .. 17 ] enumerated code over GF(2) Covering radius: [ 16 .. 17 ] number 22 out of 64 C: a cyclic [35,1,35]17 enumerated code over GF(2) Covering radius: 17 number 38 out of 64 C: a cyclic [35,0,35]35 enumerated code over GF(2) Covering radius: 35 number 7 out of 64 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ LogTo("/home/wdj/gapfiles/codes/covering_codesn35i13.log"); CCs:=CyclicCodes(35,GF(2));; C:=CCs[13]; MinimumDistance(C); C; #CoveringRadius(C); IncreaseCoveringRadiusLowerBound(C); LogTo();