Binary codes created by doubling construction, including quasi-perfect ones with distance d = 4, are investigated. All [17·2^(r-6), 17·2^(r-6) - r, 4] quasi-perfect codes are classified. Weight spectrum of the codes dual to quasi-perfect ones with d = 4 is obtained. The automorphism group Aut(C) of codes obtained by doubling construction is studied. A subgroup of Aut(C) is described and it is proved that the subgroup coincides with Aut(C) if the starting matrix of doubling construction has an odd number of columns. (It happens for all quasi-perfect codes with d = 4 except for Hamming one.) The properness and t-properness for error detection of codes obtained by doubling construction are considered.
New Results on Binary Codes Obtained by Doubling Construction
Stefano Marcugini;Fernanda Pambianco
2018
Abstract
Binary codes created by doubling construction, including quasi-perfect ones with distance d = 4, are investigated. All [17·2^(r-6), 17·2^(r-6) - r, 4] quasi-perfect codes are classified. Weight spectrum of the codes dual to quasi-perfect ones with d = 4 is obtained. The automorphism group Aut(C) of codes obtained by doubling construction is studied. A subgroup of Aut(C) is described and it is proved that the subgroup coincides with Aut(C) if the starting matrix of doubling construction has an odd number of columns. (It happens for all quasi-perfect codes with d = 4 except for Hamming one.) The properness and t-properness for error detection of codes obtained by doubling construction are considered.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
