Algebraic Decoding of Some Quadratic Residue Codes With Weak Locators

作者：Lee, Chong Dao^*; Chen, Yan Haw; Trieu Kien Truong; Chang, Yaotsu

来源：IEEE Transactions on Information Theory, 2015, 61(3): 1179-1187.

DOI：10.1109/TIT.2015.2388753

• Algebraic decoding
• error-locator polynomials
• syndromes
• ternary quadratic residue codes
• weak-locator polynomials

In this paper, an explicit expression of the weak-locator polynomial for p-ary quadratic residue codes is presented by a modification of the Feng-Tzeng matrix method. The differences between the modified version and the original Feng-Tzeng matrix are that in the new matrix, not every entry is a syndrome, and every syndrome entry is a known syndrome. By utilizing this technique, an algebraic decoding of the ternary (61, 30, 12) quadratic residue code is proposed. This new result has never been seen in the literature to our knowledge. An advantage of the proposed decoding algorithm is that in general the obtained weak-locator polynomials can decode efficiently not only all the error patterns of weights four and five, but also some error patterns of weight six.

• 出版日期2015-3
• 单位中山大学