[et_pb_section fb_built=”1″ theme_builder_area=”post_content” _builder_version=”4.27.7″ _module_preset=”default”][et_pb_row column_structure=”1_3,2_3″ _builder_version=”4.27.4″ _module_preset=”default” custom_padding=”40px|||||” global_colors_info=”{}” theme_builder_area=”post_content”][et_pb_column type=”1_3″ _builder_version=”4.27.4″ _module_preset=”default” global_colors_info=”{}” theme_builder_area=”post_content”][et_pb_heading title=”Decreasing Monomial Codes over the Quaternary Ring Z4″ _builder_version=”4.27.7″ _module_preset=”default” title_font=”|700|on||||||” title_text_color=”gcid-body-color” title_font_size=”41px” custom_margin=”|-828px|25px|||” hover_enabled=”0″ global_colors_info=”{%22gcid-body-color%22:%91%22title_text_color%22%93}” theme_builder_area=”post_content” sticky_enabled=”0″][\/et_pb_heading][et_pb_image src=”http:\/\/cvsc.upcebu.edu.ph\/wp-content\/uploads\/2026\/07\/Sardan-Journal-of-Physics.jpg” title_text=”JPCS FC 0519″ _builder_version=”4.27.7″ _module_preset=”default” hover_enabled=”0″ box_shadow_style=”preset2″ global_colors_info=”{}” theme_builder_area=”post_content” sticky_enabled=”0″][\/et_pb_image][\/et_pb_column][et_pb_column type=”2_3″ _builder_version=”4.27.4″ _module_preset=”default” global_colors_info=”{}” theme_builder_area=”post_content”][et_pb_text _builder_version=”4.27.7″ _module_preset=”default” text_font_size=”15px” text_line_height=”1.2em” custom_padding=”118px|||||” hover_enabled=”0″ global_colors_info=”{}” theme_builder_area=”post_content” sticky_enabled=”0″]<\/p>\n
Lead Researcher(s): <\/strong>Keneth Josua P. Sardan and Virgilio P. Sison Abstract\/summary:<\/strong> This paper extends the work on monomial codes over F2 [Bardet, et al. [1]] to the ring Z4, developing an algebraic framework for constructing and analyzing quaternary monomial codes. In particular, the decreasing monomial codes in Rm, the quotient ring over the polynomial ring Z4 with indeterminates x0, …, xm\u22121 modulo the ideal (x 2 0\u2212x0, …, x2 m\u22121\u2212xm\u22121), defined via evaluations ordered by a refined partial order on monomials to determine minimal generating sets. A key result is the characterization of quaternary Reed-Muller codes RM(r, m) as decreasing monomial codes, generated by monomials selected according to degree and coefficient constraints. This construction enables systematic code generation, and examples computed in MAGMA confirm that several of the resulting codes meet known upper bounds.<\/span><\/p>\n [\/et_pb_text][et_pb_button button_text=”Downloadable PDF” _builder_version=”4.27.7″ _module_preset=”default” theme_builder_area=”post_content” url_new_window=”on” button_url=”https:\/\/iopscience.iop.org\/article\/10.1088\/1742-6596\/3114\/1\/012013\/pdf” custom_button=”on” button_text_color=”#8A1538″ hover_enabled=”0″ sticky_enabled=”0″][\/et_pb_button][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":" Lead Researcher(s): Keneth Josua P. Sardan and Virgilio P. SisonStatus: Published Abstract\/summary: This paper extends the work on monomial codes over F2 [Bardet, et al. [1]] to the ring Z4, developing an algebraic framework for constructing and analyzing quaternary monomial codes. In particular, the decreasing monomial codes in Rm, the quotient ring over the polynomial […]<\/p>\n","protected":false},"author":7,"featured_media":0,"template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"project_category":[76,40,34],"project_tag":[],"class_list":["post-3404","project","type-project","status-publish","hentry","project_category-cos-proceedings","project_category-proceedings","project_category-recent-publications"],"_links":{"self":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project\/3404","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project"}],"about":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/types\/project"}],"author":[{"embeddable":true,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/users\/7"}],"version-history":[{"count":2,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project\/3404\/revisions"}],"predecessor-version":[{"id":3408,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project\/3404\/revisions\/3408"}],"wp:attachment":[{"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/media?parent=3404"}],"wp:term":[{"taxonomy":"project_category","embeddable":true,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project_category?post=3404"},{"taxonomy":"project_tag","embeddable":true,"href":"https:\/\/cvsc.upcebu.edu.ph\/index.php\/wp-json\/wp\/v2\/project_tag?post=3404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Status:<\/strong> Published<\/p>\n