Partial Permutation Decoding for Several Families of Linear and <inline-formula> <tex-math notation="LaTeX">${\mathbb{Z}}_4$ </tex-math> </inline-formula>-Linear Codes

Decoding of Z2S Linear Generalized Kerdock Codes

“…A variety of strategies have been used in designing decoders for codes over rings, as mentioned in [25]. These include the algebraic (syndrome) decoding approach [26], the lifting decoder technique, introduced in [27] and extended in [28], the coset decomposition approach [29], and the permutation decoding [25,30,31]. Several algebraic decoders of codes over rings were presented in [2,[32][33][34][35].…”

SISO Decoding of ℤ4 Linear Kerdock and Preparata Codes

“…Common approaches for designing decoders for codes over rings include [23] the algebraic (syndrome) decoding of linear codes [24], the lifting decoder technique [25,26], the partitioning of a code into the subcode and its cosets (a.k.a. the coset decomposition approach), introduced by Conway and Sloane in [27] (which works for both linear and nonlinear codes), and the permutation decoding [23,28,29]. Most of the soft decision decoders employ some form of the coset decomposition approach.…”