Some Properties of Subspaces over Residue Class Rings
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Abstract
Let denote the residue class ring where
is a prime number and
is a positive integer. For
, a free submodule of the
-module
that has a basis is called a subspace of
. In this paper, we present some properties of subspaces regarding their dimensions and the joins of subspaces of
.
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References
Calderbank AR, McGuire G, Kumar PV, Helleseth T. Cyclic codes over Z_4, locator polynomials and Newton’s identities. IEEE Trans Inform Theory. 1996;42:217-26.
Helleseth T. Codes over Z_4. In: Alt, H. (eds) Computational Discrete Mathematics. Lecture Notes in Computer Science, vol 2122. Berlin, Heidelberg: Springer; 2001.
Van Lint JH. Codes over Z_4. In: Introduction to Coding Theory. Graduate Texts in Mathematics, vol 86. Berlin, Heidelberg: Springer; 1999.
Kyureghyan G, Kwon SM. Codes over the ring Z_p^s: Bounds on the minimum distance. Finite Fields Appl. 2010; 16(2):144-163.
Huang LP, Lv B, Wang K. Automorphisms of Grassmann graphs over a residue class ring. Discrete Math. 2020;343(4):111693.
Huang, LP, Lv B, Wang K. Erdos-Ko-Rado theorem, Grassmann graphs and p^s-Kneser graphs for vector spaces over a residue class ring. J Comb Theory Ser A. 2019;164:125-158.
Guo J. Erdos-Ko-Rado theorem for matrices over residue class rings. Graphs Combin. 2021;37(6):1-14.
Huang LP. Generalized bilinear forms graphs and MRD codes over a residue class ring. Finite Fields Appl. 2018;51:306-324.
Huang LP, Su H, Tang G, Wang JB. Bilinear forms graphs over residue class rings. Linear Algebra Appl. 2017;253:13-32.
Li F, Wang K, Guo J. More on symplectic graphs modulo p^n. Linear Algebra Appl. 2017;438(6):2651-2660.
Meemark Y, Prinyasart T. On symplectic graphs modulo p^n. Discrete Math. 2011;311(17):1874-1878.
McDonald BR. Finite Rings with Identity. New York: Marcel Dekker; 1974.
McDonald BR. Geometric Algebra over Local Rings. New York: Marcel Dekker; 1976.
McCoy NH.: Rings and Ideals. Washington, DC: The Mathematical Association of America; 1948.
Wan ZX. Lectures on Finite Fields and Galois Rings. Singapore: World Scientific Publishing Company; 2003.
Sirisuk S, Meemark Y. Generalized symplectic graphs and generalized orthogonal graphs over finite commutative rings. Linear Multilinear Algebra. 2019;67(12):2427-2450.