Optimal Ternary (10, 7) Error-Correcting Codes [PDF]
Michael J. Letourneau and Sheridan K. Houghten, May 2002.
We describe a series of exhaustive computer searches to determine the maximum number of words in ternary codes of length 10 and minimum distance 7, and to find all such optimal codes. We show that there are exactly 10 inequivalent (10, 14, 7) ternary codes. We prove A_3(10, 7) = 14 by showing that none of the (10, 14, 7)_3 codes can be extended to a (10, 15, 7)_3 code, thereby also giving A_3(11, 7)=42 and A_3(12, 7)=126. We present estimates related to the time required to establish the exact value of A_3(11, 7).