lower bound:  72 
upper bound:  77 
Construction of a linear code [123,9,72] over GF(3): [1]: [121, 10, 72] Cyclic Linear Code over GF(3) CyclicCode of length 121 with generating polynomial x^111 + x^109 + x^108 + x^106 + 2*x^105 + x^104 + x^103 + 2*x^102 + x^100 + x^99 + 2*x^95 + 2*x^94 + x^92 + 2*x^91 + x^90 + x^89 + x^88 + 2*x^86 + x^85 + x^84 + 2*x^83 + x^82 + 2*x^81 + x^79 + 2*x^78 + 2*x^77 + x^76 + x^75 + x^74 + 2*x^72 + 2*x^71 + 2*x^70 + x^69 + 2*x^68 + x^67 + x^66 + 2*x^63 + x^58 + 2*x^57 + x^56 + 2*x^53 + 2*x^52 + x^51 + x^50 + 2*x^49 + x^48 + x^47 + 2*x^46 + 2*x^45 + 2*x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + 2*x^36 + x^35 + 2*x^34 + 2*x^33 + x^32 + 2*x^31 + 2*x^30 + x^29 + x^28 + x^26 + x^25 + x^23 + x^22 + 2*x^19 + 2*x^18 + 2*x^17 + x^13 + 2*x^12 + 2*x^10 + x^8 + 2*x^6 + x^4 + 2*x^3 + 2*x^2 + x + 2 [2]: [123, 10, 72] Linear Code over GF(3) PadCode [1] by 2 [3]: [123, 9, 72] Linear Code over GF(3) Subcode of [2] last modified: 20011217
Lb(123,9) = 72 is found by taking a subcode of: Lb(123,10) = 72 is found by lengthening of: Lb(121,10) = 72 dB Ub(123,9) = 77 is found by considering shortening to: Ub(122,8) = 77 is found by considering truncation to: Ub(121,8) = 76 LP
dB: M.A. de Boer, A ternary [91,9,54] code, preprint, 9504; A dual quaternary BCH code, 9502. Codes spanned by quadratic and Hermitian forms, IEEE Trans. Inform. Theory 42 (1996) 16001604.
Notes
