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公开(公告)号：US20220021401A1
公开(公告)日：2022-01-20
申请号：US16929983
申请日：2020-07-15
Applicant: SAMSUNG ELECTRONICS CO., LTD.
Inventor： AVNER DOR , Amit Berman , Ariel Doubchak , Elik Almog Sheffi , Yaron Shany
Abstract: A method of performing division operations in an error correction code includes the steps of receiving an output ω∈F†{0} wherein F=GF(2r) is a Galois field of 2r elements, ω=Σ0≤i≤r−1βi×αi wherein α is a fixed primitive element of F, and βi∈GF(2), wherein K=GF(2s) is a subfield of F, and {1, α} is a basis of F in a linear subspace of K; choosing a primitive element δ∈K, wherein ω=ω1+α×ω2, ω1=Σ0≤i≤s−1γi×δi∈K, ω2=Σ0≤i≤s−1γi+s×δi∈K, and γ=[γ0, . . . , γr−1]T∈GF(2)r; accessing a first table with ω1 to obtain ω3=ω1−1, computing ω2×ω3 in field K, accessing a second table with ω2=ω3 to obtain (1+α×ω2×ω3)−1=ω4+α×ω5, wherein ω−1=(ω1×(1+α×ω2×ω3))−1=ω3×(ω4+α×ω5)=ω3×ω4+α×ω3×ω5; and computing products ω3×ω4 and ω3×ω5 to obtain ω−1=Σ0≤i≤s−1θi×δi+α·Σi≤i≤s−1θi+s=δi where θi∈GF(2).
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公开(公告)号：US11438013B2
公开(公告)日：2022-09-06
申请号：US16929983
申请日：2020-07-15
Applicant: SAMSUNG ELECTRONICS CO., LTD.
Inventor： Avner Dor , Amit Berman , Ariel Doubchak , Elik Almog Sheffi , Yaron Shany
Abstract: A method of performing division operations in an error correction code includes the steps of receiving an output ω∈F†{0} wherein F=GF(2r) is a Galois field of 2r elements, ω=Σ0≤i≤r−1βi×αi wherein α is a fixed primitive element of F, and βi∈GF(2), wherein K=GF(2s) is a subfield of F, and {1, α} is a basis of F in a linear subspace of K; choosing a primitive element δ∈K, wherein ω=ω1+α×ω2, ω1=Σ0≤i≤s−1 γi×δi∈K, ω2=Σ0≤i≤s−1 γi+s×δi∈K, and γ=[γ0, . . . , γr−1]T∈GF(2)r; accessing a first table with ω1 to obtain ω3=ω1−1, computing ω2×ω3 in field K, accessing a second table with ω2=ω3 to obtain (1+α×ω2×ω3)−1=ω4+α×ω5, wherein ω−1=(ω1×(1+α×ω2×ω3))−1=ω3×(ω4+α×ω5)=ω3×ω4+α×ω3×ω5; and computing products ω3×ω4 and ω3×ω5 to obtain ω−1=Σ0≤i≤s−1θi×δi+α·Σi≤i≤s−1θi+s=δi where θi∈GF(2).
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