Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Several theorems are presented which characterize Goppa codes having the property of becoming cyclic when an overall parity cheek is added. If such a Goppa code has location set L = GF (q^{m}) and a Goppa polynomial g(z) that is irreducible over GF(q^{m}) , then g(z) must be a quadratic. Goppa codes defined by (z- \beta)^{a} and location set L with cardinality n such that n+l|q^{m}-1 are considered along with their subcodes. A sufficient condition on L is derived for the extended codes to become cyclic. This condition is also necessary when a = 1. The construction of L for different n satisfying the stated condition is investigated in some detail. Some irreversible Goppa codes have been shown to become cyclic when extended by an overall parity check.
['Kenneth K. Tzeng', 'Chie Y. Yu']
I am writing a research paper on a idea Characterization theorems for extending Goppa codes to cyclic codes (Corresp.)
[{"from": "human", "value": "I am writing a research paper on a idea Characterization theorems for extending Goppa codes to cyclic codes (Corresp.)"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Several theorems are presented which characterize Goppa codes having the property of becoming cyclic when an overall parity cheek is added. If such a Goppa code has location set L = GF (q^{m}) and a Goppa polynomial g(z) that is irreducible over GF(q^{m}) , then g(z) must be a quadratic. Goppa codes defined by (z- \\beta)^{a} and location set L with cardinality n such that n+l|q^{m}-1 are considered along with their subcodes. A sufficient condition on L is derived for the extended codes to become cyclic. This condition is also necessary when a = 1. The construction of L for different n satisfying the stated condition is investigated in some detail. Some irreversible Goppa codes have been shown to become cyclic when extended by an overall parity check."}]