EXHIBIT 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of The Dixie Group, Inc. (the "Company") on Form 10-Q for the quarter ended March 30, 2024, as filed with the Securities and Exchange Commission on the date hereof (the "Report"), I, Daniel K. Frierson, the Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of my knowledge:

(1) the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ DANIEL K. FRIERSON

Daniel K. Frierson, Chief Executive Officer

Date: May 3, 2024

A signed original of this written statement required by Section 906 has been provided to The Dixie Group, Inc. and will be retained by The Dixie Group, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.