lower bound: | 100 |
upper bound: | 105 |
Construction of a linear code [232,18,100] over GF(2): [1]: [238, 19, 104] Quasicyclic of degree 7 Linear Code over GF(2) QuasiCyclicCode of length 238 stacked to height 4 with generating polynomials: x^18 + x^12 + x^10 + x^8 + x^6 + 1, x^28 + x^25 + x^23 + x^20 + x^14 + x^13 + x^10 + x^9 + x^8 + x^6 + x^5 + x^4 + x + 1, x^30 + x^27 + x^25 + x^24 + x^23 + x^21 + x^19 + x^17 + x^16 + x^15 + x^13 + x^10 + x^6 + x^5 + x^4 + x^2 + x + 1, x^30 + x^28 + x^27 + x^26 + x^24 + x^22 + x^19 + x^17 + x^16 + x^14 + x^13 + x^11 + x^8 + x^6 + x^4 + x^3 + x^2 + 1, x^24 + x^23 + x^21 + x^19 + x^17 + x^16 + x^14 + x^13 + x^11 + x^10 + x^8 + x^7 + x^5 + x^3 + x + 1, x^26 + x^24 + x^23 + x^22 + x^21 + x^18 + x^17 + x^16 + x^10 + x^9 + x^8 + x^5 + x^4 + x^3 + x^2 + 1, x^30 + x^29 + x^27 + x^26 + x^23 + x^21 + x^19 + x^16 + x^14 + x^11 + x^9 + x^7 + x^4 + x^3 + x + 1, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, 0, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, 0, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 [2]: [233, 19, 100] Linear Code over GF(2) Puncturing of [1] at { 7, 131, 157, 158, 179 } [3]: [232, 18, 100] Linear Code over GF(2) Shortening of [2] at { 233 } last modified: 2014-03-29
Lb(232,18) = 96 is found by shortening of: Lb(234,20) = 96 MTS Ub(232,18) = 105 BK
MTS: Tatsuya Maruta, Mito Takenaka, Maori Shinohara & Yukie Shobara, Constructing new linear codes from pseudo-cyclic codes, pp. 292-298 in Proc. 9th International Workshop on Algebraic and Combinatorial Coding Theory(ACCT) in Kranevo, Bulgaria, 2004.
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