2019/10/29 by Michela Ceria, Ceria, Michela
Computer Science · Mathematics · #05E40 #13P10 #14G50 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1910.13189
openalex publication_date 2019/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider the four syndrom varieties \sf Ze^×, i.e. the set of all error locations corresponding to errors of weight w, 0≤ w≤ 2, \sf Zns^× , the set of all \em non spurious error locations corresponding to errors of weight w, 0≤ w≤ 2, \sf Z+^× , the set of all non-spurious error locations corresponding to errors of weight w, 1≤ w≤ 2, \sf Z2^× , the set of all non-spurious error locations corresponding to errors of weight w= 2, associated to an up-to-two errors correcting binary cyclic codes. Denoting J_∗:=I(\sf Z_∗), the ideal of these syndrome varieties, \sf N_∗ := \bf N(J_∗) the \GR escalier of J_∗ w.r.t. the lex ordering with x1