Absolute minimal trellis complexities of extended codes and their dual codes of two types of linear block codes whose code length is odd are given 給出了兩類奇數(shù)碼長線性分組碼的擴展碼及其對偶碼的絕對最小網(wǎng)格圖復(fù)雜度。
As to cyclic codes over finite chain rings , we study their stucture and develop the fourier transform method to finite chain rings . the permutation groups of cyclic codes and their extended codes are investigated using their mattson - solomn polynomials 對于有限鏈環(huán)上的循環(huán)碼,我們研究了它們的結(jié)構(gòu),并把傅立葉變換的方法推廣到有限鏈環(huán),用循環(huán)碼的mattson - solomn多項式對循環(huán)碼及其擴展碼的置換群進行了研究。
The concept of good codes and proper codes for both error detection and correction is presented . it is shown that the binary perfect codes and the primitive double - error - correcting bch codes and their extended codes are proper for both error detection and correction . the primitive triple - error - correcting bch codes with length 2 " " - 1 and their extended codes are proper for odd m > 5 , not for even m > 6 本文的主要工作是把目前關(guān)于只檢錯時線性碼不可檢錯誤概率的研究推廣到同時糾錯和檢錯的情況,獲得了同時糾檢錯時線性碼不可檢錯誤概率的解析表達式,提出了糾檢錯好碼和最佳糾檢錯碼的概念,并證明了二進制完備碼及其擴展碼是最佳糾檢錯碼;糾正兩個錯誤二進制本原bch碼及其擴展碼是最佳糾檢錯碼;碼長n = 2 ~ m - 1 、糾正三個錯誤本原bch碼,當(dāng)m為大于等于5的奇數(shù)時是最佳糾檢錯碼;當(dāng)m為大于等于6的偶數(shù)時,不是最佳碼。