linear recurring sequence, standard basis, concordant standard basis, shift register.
UDC:
512.714, 512.536, 512.8, 519.725
Subject:
Algebraic coding theory, polylinear recurring sequences, standard bases (Groebner–Shirshov bases).
Main publications:
Gorbatov E. V. Standartnyi bazis polinomialnogo ideala nad kommutativnym artinovym tsepnym koltsom // Diskretnaya matematika, 16 (1) (2004), s. 52–78.
Gorbatov E. V. Standartnye bazisy soglasovannye s normirovaniem i vychisleniya v idealakh i polilineinykh rekurrentakh // Trudy mezhdunarodnoi algebraicheskoi konferentsii posvyaschennoi 250-letiyu moskovskogo universiteta, Fundamentalnaya i prikladnaya matematika, 10 (3) (2004) c. 23–72.
Gorbatov E. V., Mikhailov D. A., Mikhalev A. V., Nechaev A. A. Standartnye bazisy polinomialnykh idealov nad konechnym kommutativnym tsepnym koltsom i ikh prilozheniya // Trudy konferentsii "Matematika i bezopasnost informatsionnykh tekhnologii", MGU, oktyabr 2003, M.: MTsNMO, (2004), s. 202–217.
Gorbatov E. V. Standartnye bazisy soglasovannye s normirovaniem i
vychisleniya v idealakh i polilineinykh rekurrentakh // Trudy mezhdunarodnoi algebraicheskoi konferentsii posvyaschennoi 250-letiyu moskovskogo universiteta, Fundamentalnaya i prikladnaya matematika, 10, (3) (2004), s. 23–71.
Gorbatov E. V. Multiplikativnye poryadki na odnochlenakh // Trudy mezhdunarodnyi seminar po kompyuternoi algebre i informatike, posvyaschennogo 30-letiyu laboratorii vychislitelnykh metodov MGU, Fundamentalnaya i prikladnaya matematika, (2005).
E. V. Gorbatov, “The standard basis of a polynomial ideal over a commutative Artinian chain ring”, Diskr. Mat., 16:1 (2004), 52–78; Discrete Math. Appl., 14:1 (2004), 75–101
E. V. Gorbatov, “Standard bases concordant with the norm and computations in ideals and polylinear recurring sequences”, Fundam. Prikl. Mat., 10:3 (2004), 23–71; J. Math. Sci., 139:4 (2006), 6672–6707
E. V. Gorbatov, A. A. Nechaev, “Cyclic families of polylinear recurring sequences over quasi-Frobenius modules”, Uspekhi Mat. Nauk, 57:4(346) (2002), 167–168; Russian Math. Surveys, 57:4 (2002), 803–804
